Provisional IRA Belfast Brigade was created in 1969.

The Old IRA (1919-1922) wanted a free Ireland from the British.

The Provisional IRA (1969-1998) wanted a united Ireland free from British control.

and The Real IRA (1972-1997) wanted the British out of Northern Ireland and were willing to do anything for it.

As Margaret Thatcher did not defeat the IRA I don't expect it will.

The IRA was never defeated. The Provisional IRA embarked on a thirty year armed campaign against the British presence in Northern Ireland that claimed 1707 lives. In 1997 it announced a ceasefire which effectively marked the end of its campaign. In 2005 it formally announced the end of its campaign and destroyed much of its weaponry under international supervision. The movement's political wing, Provisional Sinn Féin, is a growing electoral force in both Northern Ireland and the Republic.

The IRA disbanded in 1923 after the civil war.

The modern equivalents of the IRA such as the Provisional IRA decommissioned their arms and ended their service in 2005.

Splinter groups like the Real IRA and Continuity IRA are still active, just about. But are not currently engaged in an armed campaign.

The Provisional Irish republican army (IRA), was formed in 1969 after it split from the Official Irish republican army (OIRA) over the OIRAs failure to protect Irish nationalist areas from attack by british loyalists and the police the Royal ulster constabulary (RUC). The Real Irish republican army (RIRA) split from the provisional IRA in 1997 after the IRA called a ceasefire and entered into the northern Ireland peace process. The Real IRA (RIRA) continue to use armed struggle to free northern Ireland from british rule, they attack british military, political and economic targets throughout northern Ireland and are believed to be preparing to bomb the british mainland. The Provisional IRA have ceased their armed campaign, have decommisioned most of their weapons and have moved into peaceful politics through their political party Sinn Fein. The Real IRA regard the provisionals as sell outs of republicanism and believe themselves to be the legitimate army in the struggle for Irish freedom.

In short, the Real IRA are still fighting, the Provisional IRA have stopped.