Theorem alrimd 1541

Description: Deduction from Theorem 19.21 of [Margaris] p. 90. (Contributed by Mario Carneiro, 24-Sep-2016.)

Hypotheses

Ref	Expression
alrimd.1	|- F/ x ph
alrimd.2	|- F/ x ps
alrimd.3	|- ( ph -> ( ps -> ch ) )

Assertion

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

Proof of Theorem alrimd

Step	Hyp	Ref	Expression
1		alrimd.1	. 2 |- F/ x ph
2		alrimd.2	. . 3 |- F/ x ps
3	2	a1i 9	. 2 |- ( ph -> F/ x ps )
4		alrimd.3	. 2 |- ( ph -> ( ps -> ch ) )
5	1, 3, 4	alrimdd 1540	1 |- ( ph -> ( ps -> A. x ch ) )

Syntax hints:   -> wi 4   A.wal 1282   F/wnf 1389

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-5 1376  ax-gen 1378  ax-4 1440

This theorem depends on definitions:  df-bi 115  df-nf 1390

This theorem is referenced by:  euexex  2026  ralrimd  2439