Theorem jcai 311

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 13	. 2 |- ( ph -> ch )
4	1, 3	jca 306	1 |- ( ph -> ( ps /\ ch ) )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108

This theorem is used by:  dfifp2dc  994  reu6  3015  f1ocnv2d  6294  f1o3d  6298  nnoddn2prm  13039