Theorem jca3

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

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

Proof

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