Theorem 3jca

Description: Join consequents with conjunction. (Contributed by NM, 9-Apr-1994)

	Ref	Expression
Hypotheses	3jca.1	|- ( ph -> ps )
	3jca.2	|- ( ph -> ch )
	3jca.3	|- ( ph -> th )
Assertion	3jca	|- ( ph -> ( ps /\ ch /\ th ) )

Proof

Step	Hyp	Ref	Expression
1		3jca.1	|- ( ph -> ps )
2		3jca.2	|- ( ph -> ch )
3		3jca.3	|- ( ph -> th )
4	1 2 3	jca31	|- ( ph -> ( ( ps /\ ch ) /\ th ) )
5		df-3an	|- ( ( ps /\ ch /\ th ) <-> ( ( ps /\ ch ) /\ th ) )
6	4 5	sylibr	|- ( ph -> ( ps /\ ch /\ th ) )