Theorem jca2r 34139

Description: Inference conjoining the consequents of two implications. (Contributed by Rodolfo Medina, 17-Oct-2010.)

Hypotheses

Ref	Expression
jca2r.1	|- ( ph -> ( ps -> ch ) )
jca2r.2	|- ( ps -> th )

Assertion

Ref	Expression
jca2r	|- ( ph -> ( ps -> ( th /\ ch ) ) )

Proof of Theorem jca2r

Step	Hyp	Ref	Expression
1		jca2r.2	. . 3 |- ( ps -> th )
2	1	a1i 11	. 2 |- ( ph -> ( ps -> th ) )
3		jca2r.1	. 2 |- ( ph -> ( ps -> ch ) )
4	2, 3	jcad 555	1 |- ( ph -> ( ps -> ( th /\ ch ) ) )

Syntax hints:   -> wi 4   /\ wa 384

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 197  df-an 386

This theorem is referenced by:  prter2  34166