Theorem jca31 520

Description: Join three consequents. (Contributed by Jeff Hankins, 1-Aug-2009.)

Hypotheses

Ref	Expression
jca31.1	|- (ph -> ps)
jca31.2	|- (ph -> ch)
jca31.3	|- (ph -> th)

Assertion

Ref	Expression
jca31	|- (ph -> ((ps /\ ch) /\ th))

Proof of Theorem jca31

Step	Hyp	Ref	Expression
1		jca31.1	. . 3 |- (ph -> ps)
2		jca31.2	. . 3 |- (ph -> ch)
3	1, 2	jca 518	. 2 |- (ph -> (ps /\ ch))
4		jca31.3	. 2 |- (ph -> th)
5	3, 4	jca 518	1 |- (ph -> ((ps /\ ch) /\ th))

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:  3jca  1132  syl21anc  1181  f1oiso2  5501