The Attack on the White House was a pivotal moment in history essentially governing the fate of the future. A whole new timeline of events were spawned out of this moment changing all events after 1973.
With Trask not killed the dark Sentinel future was prevented from existing, changing history mostly for the better. Trask however was put jail by President Nixon, in Magneto's old cell at the pentagon. Magneto would go on the run and eventually meet Magda Gurzsky. Mystique would go on to become a hero for young mutants but she would also go into hiding. Wolverine would be fished out of the river and would eventually be found by William Stryker and taken to Alkali Lake. Charles and Beast would reopen Xavier's school for new mutants.
As a result of this event in 2023 Wolverine would wake up in the X-Mansion, regaining his consciousness and memories from his travels to the 70's. He would find the school running normally and that Professor X, Cyclops, Jean Grey, Storm, Rogue, Iceman, Beast, Shadowcat and Colossus all alive and well.