Theorem bj-nfalt 12664

Description: Closed form of nfal 1538 (copied from set.mm). (Contributed by BJ, 2-May-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-nfalt	|- ( A. x F/ y ph -> F/ y A. x ph )

Proof of Theorem bj-nfalt

Step	Hyp	Ref	Expression
1		bj-hbalt 12663	. . . 4 |- ( A. x ( ph -> A. y ph ) -> ( A. x ph -> A. y A. x ph ) )
2	1	alimi 1414	. . 3 |- ( A. y A. x ( ph -> A. y ph ) -> A. y ( A. x ph -> A. y A. x ph ) )
3	2	alcoms 1435	. 2 |- ( A. x A. y ( ph -> A. y ph ) -> A. y ( A. x ph -> A. y A. x ph ) )
4		df-nf 1420	. . 3 |- ( F/ y ph <-> A. y ( ph -> A. y ph ) )
5	4	albii 1429	. 2 |- ( A. x F/ y ph <-> A. x A. y ( ph -> A. y ph ) )
6		df-nf 1420	. 2 |- ( F/ y A. x ph <-> A. y ( A. x ph -> A. y A. x ph ) )
7	3, 5, 6	3imtr4i 200	1 |- ( A. x F/ y ph -> F/ y A. x ph )

Syntax hints:   -> wi 4   A.wal 1312   F/wnf 1419

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-7 1407  ax-gen 1408

This theorem depends on definitions:  df-bi 116  df-nf 1420

This theorem is referenced by: (None)