Theorem alimd 2081

Description: Deduction form of Theorem 19.20 of [Margaris] p. 90, see alim 1738. (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	nf5ri 2065	. 2 |- ( ph -> A. x ph )
3		alimd.2	. 2 |- ( ph -> ( ps -> ch ) )
4	2, 3	alimdh 1745	1 |- ( ph -> ( A. x 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:  alrimdd  2083  nfald  2165  mo3  2507  2mo  2551  axpowndlem3  9421  axext4dist  31706  bj-mo3OLD  32832  pm11.71  38597