Theorem axc112 2019

Description: Same as axc11 2147 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 1932	. . 3 |- ( y = x -> ( A. x ph -> A. y ( y = x -> ph ) ) )
2	1	sps 1942	. 2 |- ( A. y y = x -> ( A. x ph -> A. y ( y = x -> ph ) ) )
3		pm2.27 40	. . 3 |- ( y = x -> ( ( y = x -> ph ) -> ph ) )
4	3	al2imi 1686	. 2 |- ( A. y y = x -> ( A. y ( y = x -> ph ) -> A. y ph ) )
5	2, 4	syld 45	1 |- ( A. y y = x -> ( A. x ph -> A. y ph ) )

Syntax hints:   -> wi 4   A.wal 1441

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-12 1932

This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1663

This theorem is referenced by:  axc16g  2022  axc11n  2142  axc11nALT  2143  axc11  2147  hbae  2148  dral1  2158  dral1ALT  2159  axpowndlem3  9021  bj-axc11nv  31341  bj-axc11v  31344  bj-dral1v  31351  bj-hbaeb2  31413