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Theorem baibr 829
Description: Move conjunction outside of biconditional. (Contributed by NM, 11-Jul-1994.)
Hypothesis
Ref Expression
baib.1 (𝜑 ↔ (𝜓𝜒))
Assertion
Ref Expression
baibr (𝜓 → (𝜒𝜑))

Proof of Theorem baibr
StepHypRef Expression
1 baib.1 . . 3 (𝜑 ↔ (𝜓𝜒))
21baib 828 . 2 (𝜓 → (𝜑𝜒))
32bicomd 129 1 (𝜓 → (𝜒𝜑))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 97  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  rbaibr  831  pm5.44  834  exmoeu2  1948  ssnelpss  3289  r19.9rmv  3313  dfopg  3547  brinxp  4408  elioo5  8802
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