Theorem jca2 306

Description: Inference conjoining the consequents of two implications. (Contributed by Rodolfo Medina, 12-Oct-2010.)

Hypotheses

Ref	Expression
jca2.1	|- ( ph -> ( ps -> ch ) )
jca2.2	|- ( ps -> th )

Assertion

Ref	Expression
jca2	|- ( ph -> ( ps -> ( ch /\ th ) ) )

Proof of Theorem jca2

Step	Hyp	Ref	Expression
1		jca2.1	. 2 |- ( ph -> ( ps -> ch ) )
2		jca2.2	. . 3 |- ( ps -> th )
3	2	a1i 9	. 2 |- ( ph -> ( ps -> th ) )
4	1, 3	jcad 305	1 |- ( ph -> ( ps -> ( ch /\ th ) ) )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107

This theorem is referenced by:  txcn  12915