Theorem baibr 872

Description: Move conjunction outside of biconditional. (Contributed by NM, 11-Jul-1994.)

Hypothesis

Ref	Expression
baib.1	⊢ (φ ↔ (ψ ∧ χ))

Assertion

Ref	Expression
baibr	⊢ (ψ → (χ ↔ φ))

Proof of Theorem baibr

Step	Hyp	Ref	Expression
1		baib.1	. . 3 ⊢ (φ ↔ (ψ ∧ χ))
2	1	baib 871	. 2 ⊢ (ψ → (φ ↔ χ))
3	2	bicomd 192	1 ⊢ (ψ → (χ ↔ φ))

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:  rbaibr  874  pm5.44  877  exmoeu2  2247  ssnelpss  3614  brinxp  4837