Theorem alrimdv 1633

Description: Deduction from Theorem 19.21 of [Margaris] p. 90. (Contributed by NM, 10-Feb-1997.)

Hypothesis

Ref	Expression
alrimdv.1	|- (ph -> (ps -> ch))

Assertion

Ref	Expression
alrimdv	|- (ph -> (ps -> A.xch))

Distinct variable groups:   ph,x   ps,x

Allowed substitution hint:   ch(x)

Proof of Theorem alrimdv

Step	Hyp	Ref	Expression
1		ax-17 1616	. 2 |- (ph -> A.xph)
2		ax-17 1616	. 2 |- (ps -> A.xps)
3		alrimdv.1	. 2 |- (ph -> (ps -> ch))
4	1, 2, 3	alrimdh 1587	1 |- (ph -> (ps -> A.xch))

Syntax hints:   -> wi 4  A.wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1546  ax-5 1557  ax-17 1616

This theorem is referenced by:  funcnvuni  5162  eqfnfv  5393