Theorem jcai 289

Description: Deduction replacing implication with conjunction.

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 26	. 2 |- (ph -> ch)
4	1, 3	jca 288	1 |- (ph -> (ps /\ ch))

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  reu3 1934  opth 2793  en3d 4407  iintlem1 10603  iint 10605

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

Copyright terms: Public domain