Theorem alimd 1509

Description: Deduction from Theorem 19.20 of [Margaris] p. 90. (Contributed by Mario Carneiro, 24-Sep-2016.)

Hypotheses

Ref	Expression
alimd.1	|- F/ x ph
alimd.2	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
alimd	|- ( ph -> ( A. x ps -> A. x ch ) )

Proof of Theorem alimd

Step	Hyp	Ref	Expression
1		alimd.1	. . 3 |- F/ x ph
2	1	nfri 1507	. 2 |- ( ph -> A. x ph )
3		alimd.2	. 2 |- ( ph -> ( ps -> ch ) )
4	2, 3	alimdh 1455	1 |- ( ph -> ( A. x ps -> A. x ch ) )

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-5 1435  ax-gen 1437  ax-4 1498

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

This theorem is referenced by:  alrimdd  1597  moim  2078  ralimdaa  2532  setindft  13847