Theorem mpbi2and

Description: Detach a conjunction of truths in a biconditional. (Contributed by NM, 6-Nov-2011) (Proof shortened by Wolf Lammen, 24-Nov-2012)

	Ref	Expression
Hypotheses	mpbi2and.1	|- ( ph -> ps )
	mpbi2and.2	|- ( ph -> ch )
	mpbi2and.3	|- ( ph -> ( ( ps /\ ch ) <-> th ) )
Assertion	mpbi2and	|- ( ph -> th )

Proof

Step	Hyp	Ref	Expression
1		mpbi2and.1	|- ( ph -> ps )
2		mpbi2and.2	|- ( ph -> ch )
3		mpbi2and.3	|- ( ph -> ( ( ps /\ ch ) <-> th ) )
4	1 2	jca	|- ( ph -> ( ps /\ ch ) )
5	4 3	mpbid	|- ( ph -> th )