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Theorem rbaib 907
Description: Move conjunction outside of biconditional. (Contributed by Mario Carneiro, 11-Sep-2015.)
Hypothesis
Ref Expression
baib.1 (𝜑 ↔ (𝜓𝜒))
Assertion
Ref Expression
rbaib (𝜒 → (𝜑𝜓))

Proof of Theorem rbaib
StepHypRef Expression
1 baib.1 . . 3 (𝜑 ↔ (𝜓𝜒))
2 ancom 264 . . 3 ((𝜓𝜒) ↔ (𝜒𝜓))
31, 2bitri 183 . 2 (𝜑 ↔ (𝜒𝜓))
43baib 905 1 (𝜒 → (𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  reusv1  4383  opres  4832  cores  5046  fvres  5449  fzsplit2  9857  cnptoprest  12438
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