Theorem bianabs

Description: Absorb a hypothesis into the second member of a biconditional. (Contributed by FL, 15-Feb-2007)

	Ref	Expression
Hypothesis	bianabs.1	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜑 ∧ 𝜒 ) ) )
Assertion	bianabs	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		bianabs.1	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜑 ∧ 𝜒 ) ) )
2		ibar	⊢ ( 𝜑 → ( 𝜒 ↔ ( 𝜑 ∧ 𝜒 ) ) )
3	1 2	bitr4d	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )