Theorem jca3 34140

Description: Inference conjoining the consequents of two implications. (Contributed by Rodolfo Medina, 14-Oct-2010.)

Hypotheses

Ref	Expression
jca3.1	|- ( ph -> ( ps -> ch ) )
jca3.2	|- ( th -> ta )

Assertion

Ref	Expression
jca3	|- ( ph -> ( ps -> ( th -> ( ch /\ ta ) ) ) )

Proof of Theorem jca3

Step	Hyp	Ref	Expression
1		jca3.1	. . . . 5 |- ( ph -> ( ps -> ch ) )
2	1	imp 445	. . . 4 |- ( ( ph /\ ps ) -> ch )
3	2	a1d 25	. . 3 |- ( ( ph /\ ps ) -> ( th -> ch ) )
4		jca3.2	. . 3 |- ( th -> ta )
5	3, 4	jca2 556	. 2 |- ( ( ph /\ ps ) -> ( th -> ( ch /\ ta ) ) )
6	5	ex 450	1 |- ( ph -> ( ps -> ( th -> ( ch /\ ta ) ) ) )

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: (None)