Theorem alrimdd 1500

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 1413	. 2 |- ( ph -> ( ps -> A. x ps ) )
3		alrimdd.1	. . 3 |- F/ x ph
4		alrimdd.3	. . 3 |- ( ph -> ( ps -> ch ) )
5	3, 4	alimd 1414	. 2 |- ( ph -> ( A. x ps -> A. x ch ) )
6	2, 5	syld 40	1 |- ( ph -> ( ps -> A. x ch ) )

Syntax hints:   -> wi 4   A.wal 1241   F/wnf 1349

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-5 1336  ax-gen 1338  ax-4 1400

This theorem depends on definitions:  df-bi 110  df-nf 1350

This theorem is referenced by:  alrimd  1501