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Theorem rbaibr 869
Description: Move conjunction outside of biconditional. (Contributed by Mario Carneiro, 11-Sep-2015.)
Hypothesis
Ref Expression
baib.1 (𝜑 ↔ (𝜓𝜒))
Assertion
Ref Expression
rbaibr (𝜒 → (𝜓𝜑))

Proof of Theorem rbaibr
StepHypRef Expression
1 baib.1 . . 3 (𝜑 ↔ (𝜓𝜒))
2 ancom 262 . . 3 ((𝜓𝜒) ↔ (𝜒𝜓))
31, 2bitri 182 . 2 (𝜑 ↔ (𝜒𝜓))
43baibr 867 1 (𝜒 → (𝜓𝜑))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by: (None)
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