Theorem bianabs 850

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

Hypothesis

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

Assertion

Ref	Expression
bianabs	⊢ (φ → (ψ ↔ χ))

Proof of Theorem bianabs

Step	Hyp	Ref	Expression
1		bianabs.1	. 2 ⊢ (φ → (ψ ↔ (φ ∧ χ)))
2		ibar 490	. 2 ⊢ (φ → (χ ↔ (φ ∧ χ)))
3	1, 2	bitr4d 247	1 ⊢ (φ → (ψ ↔ χ))

Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  ceqsrexv  2973  opelopab2a  4703  ov  5596  ovg  5602