Theorem mpbir2and

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	mpbir2and.1	|- ( ph -> ch )
	mpbir2and.2	|- ( ph -> th )
	mpbir2and.3	|- ( ph -> ( ps <-> ( ch /\ th ) ) )
Assertion	mpbir2and	|- ( ph -> ps )

Proof

Step	Hyp	Ref	Expression
1		mpbir2and.1	|- ( ph -> ch )
2		mpbir2and.2	|- ( ph -> th )
3		mpbir2and.3	|- ( ph -> ( ps <-> ( ch /\ th ) ) )
4	1 2	jca	|- ( ph -> ( ch /\ th ) )
5	4 3	mpbird	|- ( ph -> ps )