Theorem rbaib 873

Description: Move conjunction outside of biconditional. (Contributed by Mario Carneiro, 11-Sep-2015.)

Hypothesis

Ref	Expression
baib.1	⊢ (φ ↔ (ψ ∧ χ))

Assertion

Ref	Expression
rbaib	⊢ (χ → (φ ↔ ψ))

Proof of Theorem rbaib

Step	Hyp	Ref	Expression
1		baib.1	. . 3 ⊢ (φ ↔ (ψ ∧ χ))
2		ancom 437	. . 3 ⊢ ((ψ ∧ χ) ↔ (χ ∧ ψ))
3	1, 2	bitri 240	. 2 ⊢ (φ ↔ (χ ∧ ψ))
4	3	baib 871	1 ⊢ (χ → (φ ↔ ψ))

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:  cador  1391