Theorem mpbiran

Description: Detach truth from conjunction in biconditional. (Contributed by NM, 27-Feb-1996)

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

Proof

Step	Hyp	Ref	Expression
1		mpbiran.1	⊢ 𝜓
2		mpbiran.2	⊢ ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ) )
3	1	biantrur	⊢ ( 𝜒 ↔ ( 𝜓 ∧ 𝜒 ) )
4	2 3	bitr4i	⊢ ( 𝜑 ↔ 𝜒 )