Theorem jcai 522

Description: Deduction replacing implication with conjunction. (Contributed by NM, 5-Aug-1993.)

Hypotheses

Ref	Expression
jcai.1	|- (ph -> ps)
jcai.2	|- (ph -> (ps -> ch))

Assertion

Ref	Expression
jcai	|- (ph -> (ps /\ ch))

Proof of Theorem jcai

Step	Hyp	Ref	Expression
1		jcai.1	. 2 |- (ph -> ps)
2		jcai.2	. . 3 |- (ph -> (ps -> ch))
3	1, 2	mpd 14	. 2 |- (ph -> ch)
4	1, 3	jca 518	1 |- (ph -> (ps /\ ch))

Syntax hints:   -> wi 4   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  reu6  3026  opkthg  4132  f1o2d  5728  enprmaplem5  6081  nchoicelem17  6306