Theorem bj-nfalt 13645

Description: Closed form of nfal 1564 (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 13644	. . . 4 |- ( A. x ( ph -> A. y ph ) -> ( A. x ph -> A. y A. x ph ) )
2	1	alimi 1443	. . 3 |- ( A. y A. x ( ph -> A. y ph ) -> A. y ( A. x ph -> A. y A. x ph ) )
3	2	alcoms 1464	. 2 |- ( A. x A. y ( ph -> A. y ph ) -> A. y ( A. x ph -> A. y A. x ph ) )
4		df-nf 1449	. . 3 |- ( F/ y ph <-> A. y ( ph -> A. y ph ) )
5	4	albii 1458	. 2 |- ( A. x F/ y ph <-> A. x A. y ( ph -> A. y ph ) )
6		df-nf 1449	. 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 1341   F/wnf 1448

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-7 1436  ax-gen 1437

This theorem depends on definitions:  df-bi 116  df-nf 1449

This theorem is referenced by: (None)