Metamath Proof Explorer


Axiom ax-7d

Description: Distinct variable version of ax-11 . (Contributed by Mario Carneiro, 14-Aug-2015)

Ref Expression
Assertion ax-7d
|- ( A. x A. y ph -> A. y A. x ph )

Detailed syntax breakdown

Step Hyp Ref Expression
0 vx
 |-  x
1 vy
 |-  y
2 wph
 |-  ph
3 2 1 wal
 |-  A. y ph
4 3 0 wal
 |-  A. x A. y ph
5 2 0 wal
 |-  A. x ph
6 5 1 wal
 |-  A. y A. x ph
7 4 6 wi
 |-  ( A. x A. y ph -> A. y A. x ph )