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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 → (φψ))

Proof of Theorem rbaib
StepHypRef Expression
1 baib.1 . . 3 (φ ↔ (ψ χ))
2 ancom 437 . . 3 ((ψ χ) ↔ (χ ψ))
31, 2bitri 240 . 2 (φ ↔ (χ ψ))
43baib 871 1 (χ → (φψ))
Colors of variables: wff setvar class
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
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