Theorem axc711to11 34202

Description: Rederivation of ax-11 2034 from axc711 34199. Note that ax-c7 34170 and ax-11 2034 are not used by the rederivation. (Contributed by NM, 18-Nov-2006.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
axc711to11	|- ( A. x A. y ph -> A. y A. x ph )

Proof of Theorem axc711to11

Step	Hyp	Ref	Expression
1		axc711toc7 34201	. . 3 |- ( -. A. y -. A. y -. A. x A. y ph -> -. A. x A. y ph )
2	1	con4i 113	. 2 |- ( A. x A. y ph -> A. y -. A. y -. A. x A. y ph )
3		axc711 34199	. . 3 |- ( -. A. y -. A. x A. y ph -> A. x ph )
4	3	alimi 1739	. 2 |- ( A. y -. A. y -. A. x A. y ph -> A. y A. x ph )
5	2, 4	syl 17	1 |- ( A. x A. y ph -> A. y A. x ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-11 2034  ax-c5 34168  ax-c4 34169  ax-c7 34170

This theorem is referenced by: (None)