Theorem alimd 1455

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 1453	. 2 |- ( ph -> A. x ph )
3		alimd.2	. 2 |- ( ph -> ( ps -> ch ) )
4	2, 3	alimdh 1397	1 |- ( ph -> ( A. x ps -> A. x ch ) )

Syntax hints:   -> wi 4   A.wal 1283   F/wnf 1390

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-5 1377  ax-gen 1379  ax-4 1441

This theorem depends on definitions:  df-bi 115  df-nf 1391

This theorem is referenced by:  alrimdd  1541  moim  2006  ralimdaa  2429  setindft  10918