Theorem alrimd 2084

Description: Deduction form of Theorem 19.21 of [Margaris] p. 90, see 19.21 2075. (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 11	. 2 |- ( ph -> F/ x ps )
4		alrimd.3	. 2 |- ( ph -> ( ps -> ch ) )
5	1, 3, 4	alrimdd 2083	1 |- ( ph -> ( ps -> A. x ch ) )

Syntax hints:   -> wi 4   A.wal 1481   F/wnf 1708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-ex 1705  df-nf 1710

This theorem is referenced by:  moexex  2541  ralrimd  2959  pssnn  8178  fiint  8237  wl-mo3t  33358  pm14.24  38633