Theorem mpbiran2

Description: Detach truth from conjunction in biconditional. (Contributed by NM, 22-Feb-1996)

	Ref	Expression
Hypotheses	mpbiran2.1	⊢ 𝜒
	mpbiran2.2	⊢ ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ) )
Assertion	mpbiran2	⊢ ( 𝜑 ↔ 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		mpbiran2.1	⊢ 𝜒
2		mpbiran2.2	⊢ ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ) )
3	2	biancomi	⊢ ( 𝜑 ↔ ( 𝜒 ∧ 𝜓 ) )
4	1 3	mpbiran	⊢ ( 𝜑 ↔ 𝜓 )