Theorem mpbir2an

Description: Detach a conjunction of truths in a biconditional. (Contributed by NM, 10-May-2005)

	Ref	Expression
Hypotheses	mpbir2an.1	$$⊢\psi$$
	mpbir2an.2	$$⊢\chi$$
	mpbir2an.maj	$$⊢\phi \leftrightarrow \left(\psi \wedge \chi \right)$$
Assertion	mpbir2an	$$⊢\phi$$

Proof

Step	Hyp	Ref	Expression
1		mpbir2an.1	$$⊢\psi$$
2		mpbir2an.2	$$⊢\chi$$
3		mpbir2an.maj	$$⊢\phi \leftrightarrow \left(\psi \wedge \chi \right)$$
4	1 3	mpbiran	$$⊢\phi \leftrightarrow \chi$$
5	2 4	mpbir	$$⊢\phi$$