Theorem bj-nfalt 15194

Description: Closed form of nfal 1587 (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 15193	. . . 4 |- ( A. x ( ph -> A. y ph ) -> ( A. x ph -> A. y A. x ph ) )
2	1	alimi 1466	. . 3 |- ( A. y A. x ( ph -> A. y ph ) -> A. y ( A. x ph -> A. y A. x ph ) )
3	2	alcoms 1487	. 2 |- ( A. x A. y ( ph -> A. y ph ) -> A. y ( A. x ph -> A. y A. x ph ) )
4		df-nf 1472	. . 3 |- ( F/ y ph <-> A. y ( ph -> A. y ph ) )
5	4	albii 1481	. 2 |- ( A. x F/ y ph <-> A. x A. y ( ph -> A. y ph ) )
6		df-nf 1472	. 2 |- ( F/ y A. x ph <-> A. y ( A. x ph -> A. y A. x ph ) )
7	3, 5, 6	3imtr4i 201	1 |- ( A. x F/ y ph -> F/ y A. x ph )

Syntax hints:   -> wi 4   A.wal 1362   F/wnf 1471

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-7 1459  ax-gen 1460

This theorem depends on definitions:  df-bi 117  df-nf 1472

This theorem is referenced by: (None)