Theorem alrimdh 1587

Description: Deduction from Theorem 19.21 of [Margaris] p. 90. (Contributed by NM, 10-Feb-1997.) (Proof shortened by Andrew Salmon, 13-May-2011.)

Hypotheses

Ref	Expression
alrimdh.1	|- (ph -> A.xph)
alrimdh.2	|- (ps -> A.xps)
alrimdh.3	|- (ph -> (ps -> ch))

Assertion

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

Proof of Theorem alrimdh

Step	Hyp	Ref	Expression
1		alrimdh.2	. 2 |- (ps -> A.xps)
2		alrimdh.1	. . 3 |- (ph -> A.xph)
3		alrimdh.3	. . 3 |- (ph -> (ps -> ch))
4	2, 3	alimdh 1563	. 2 |- (ph -> (A.xps -> A.xch))
5	1, 4	syl5 28	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

This theorem is referenced by:  alrimdv  1633  ax11indn  2195