Theorem mpbir3an

Description: Detach a conjunction of truths in a biconditional. (Contributed by NM, 16-Sep-2011)

	Ref	Expression
Hypotheses	mpbir3an.1	$$⊢\psi$$
	mpbir3an.2	$$⊢\chi$$
	mpbir3an.3	$$⊢\theta$$
	mpbir3an.4	$$⊢\phi \leftrightarrow \left(\psi \wedge \chi \wedge \theta \right)$$
Assertion	mpbir3an	$$⊢\phi$$

Proof

Step	Hyp	Ref	Expression
1		mpbir3an.1	$$⊢\psi$$
2		mpbir3an.2	$$⊢\chi$$
3		mpbir3an.3	$$⊢\theta$$
4		mpbir3an.4	$$⊢\phi \leftrightarrow \left(\psi \wedge \chi \wedge \theta \right)$$
5	1 2 3	3pm3.2i	$$⊢\left(\psi \wedge \chi \wedge \theta \right)$$
6	5 4	mpbir	$$⊢\phi$$