Theorem alrimdd 1597

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

Hypotheses

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

Assertion

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

Proof of Theorem alrimdd

Step	Hyp	Ref	Expression
1		alrimdd.2	. . 3 |- ( ph -> F/ x ps )
2	1	nfrd 1508	. 2 |- ( ph -> ( ps -> A. x ps ) )
3		alrimdd.1	. . 3 |- F/ x ph
4		alrimdd.3	. . 3 |- ( ph -> ( ps -> ch ) )
5	3, 4	alimd 1509	. 2 |- ( ph -> ( A. x ps -> A. x ch ) )
6	2, 5	syld 45	1 |- ( ph -> ( 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:  alrimd  1598