Theorem axc112 1992

Description: Same as axc11 2107 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 1904	. . 3 |- ( y = x -> ( A. x ph -> A. y ( y = x -> ph ) ) )
2	1	sps 1915	. 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 1683	. 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 1435

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-12 1904

This theorem depends on definitions:  df-bi 188  df-ex 1660

This theorem is referenced by:  axc16g  1995  axc11n  2102  axc11nOLD  2103  axc11  2107  hbae  2108  dral1  2120  dral1ALT  2121  axpowndlem3  9013  bj-axc11nv  31137  bj-axc11v  31140  bj-dral1v  31147  bj-hbaeb2  31212