Theorem axc112 1884

Description: Same as axc11 2027 but with reversed antecedent. (Contributed by NM, 25-Jul-2015.)

Assertion

Ref	Expression
axc112	|- ( A. y y = x -> ( A. x ph -> A. y ph ) )

Proof of Theorem axc112

Step	Hyp	Ref	Expression
1		ax-12 1803	. . 3 |- ( y = x -> ( A. x ph -> A. y ( y = x -> ph ) ) )
2	1	sps 1814	. 2 |- ( A. y y = x -> ( A. x ph -> A. y ( y = x -> ph ) ) )
3		pm2.27 39	. . 3 |- ( y = x -> ( ( y = x -> ph ) -> ph ) )
4	3	al2imi 1616	. 2 |- ( A. y y = x -> ( A. y ( y = x -> ph ) -> A. y ph ) )
5	2, 4	syld 44	1 |- ( A. y y = x -> ( A. x ph -> A. y ph ) )

Syntax hints:   -> wi 4   A.wal 1377

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-12 1803

This theorem depends on definitions:  df-bi 185  df-ex 1597

This theorem is referenced by:  axc16g  1887  axc11n  2022  axc11nOLD  2023  axc11  2027  hbae  2028  dral1  2040  dral1ALT  2041  axpowndlem3  8976  bj-axc11nv  33614  bj-axc11v  33617  bj-dral1v  33624  bj-hbaeb2  33689