Theorem jcai 237

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 46	. 2 |- (ph -> ch)
4	1, 3	jca 236	1 |- (ph -> (ps /\ ch))

Syntax hints:   -> wi 2   /\ wa 196

This theorem is referenced by:  opth 1898  en3d 3304

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

This theorem depends on definitions:  df-bi 128  df-an 198

metamath.org