Theorem mpbiran2d

Description: Detach truth from conjunction in biconditional. Deduction form. (Contributed by Peter Mazsa, 24-Sep-2022)

	Ref	Expression
Hypotheses	mpbiran2d.1	⊢ ( 𝜑 → 𝜃 )
	mpbiran2d.2	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜒 ∧ 𝜃 ) ) )
Assertion	mpbiran2d	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		mpbiran2d.1	⊢ ( 𝜑 → 𝜃 )
2		mpbiran2d.2	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜒 ∧ 𝜃 ) ) )
3	2	biancomd	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜃 ∧ 𝜒 ) ) )
4	1 3	mpbirand	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )