The claim: Membership of the European Union guarantees rights on equal pay, sexual harassment and maternity leave, and rights for part-time workers. Those rights would be in jeopardy if Britain voted to leave.
Reality Check Verdict: The EU has been influential in the development of equality legislation but leaving would not necessarily mean those rights would be lost.
The Treaty of Rome included the commitment for member states to ensure "that men and women should receive equal pay for equal work". And the rules were strengthened following the 1975 Equal Pay Directive, and subsequent rulings by the European Court of Justice (ECJ), which have set out further what counts as equal work.
Similarly, the right of part-time workers to join occupational pension schemes was determined by rulings of the ECJ, which found that excluding them constituted indirect sex discrimination.
If Britain leaves the EU those rules could, in principle, be revoked.
However, in some cases the UK government has gone further than the rules set by the EU. For example, the 52 weeks of statutory maternity leave in the UK is considerably longer than the 14 weeks guaranteed by EU law.
Leave campaigners say there's no reason to suppose that a future British government would undermine women's rights.
But Ms Harman believes that many of the people leading the campaign for Brexit - including Boris Johnson, Nigel Farage and Iain Duncan Smith - cannot be trusted to protect women's rights.
She admits that this part of her argument is speculative, but she warns that women's rights could be eroded under the guise of pushing for deregulation and cutting red tape.
Read more: The facts behind claims in the EU debate

Hugh McGoldrick spent six days in jail after admitting falsifying drug trials on patients with sleep disorders.
The former GP, from Crossgar, County Down, was then brought before a Medical Practitioners Tribunal (MTP) hearing.
Last month, it ruled his name would be erased from the medical register but he was given 28 days to appeal.
At the time, his solicitor said McGoldrick did not accept the MTP findings and had "every intention of contesting them".
But the MTP had not received any appeal when the 28-day deadline passed on Wednesday, 29 March.
On Thursday, a spokesman for the MTP said: "We have not received any confirmation of an appeal either from the court or the doctor.
"So Dr McGoldrick's name will be removed from the register today.''
The offences took place at his Pound Lane GP practice in Downpatrick between 2007 and 2008.
The former GP was originally given a nine-month jail term and a Â£10,000 fine in June 2016, but he appealed the sentence.
His prison term was suspended and he was released from jail six days later.
Labour's former deputy leader Harriet Harman is right to say that the EU has been important in the development of UK law that affects women's right.
[NEXT_CONCEPT]
A doctor who was jailed for falsifying clinical trials for his own financial gain was finally struck off as a GP after failing to lodge an appeal.