Theorem jcai 536

Description: Deduction replacing implication with conjunction. (Contributed by NM, 15-Jul-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 15	. 2 |- ( ph -> ch )
4	1, 3	jca 532	1 |- ( ph -> ( ps /\ ch ) )

Syntax hints:   -> wi 4   /\ wa 369

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 185  df-an 371

This theorem is referenced by:  reu6  3248  f1ocnv2d  6414  onfin2  7606  mpfrcl  17720  f1o3d  26092  oddpwdc  26874  altopthsn  28129  volsupnfl  28577  mbfresfi  28579  qirropth  29390  clwlkf1clwwlklem  30663  cpmatelimp  31178  cpmatelimp2  31180