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Theorem baibr 873
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 872 . 2 (𝜓 → (𝜑𝜒))
32bicomd 140 1 (𝜓 → (𝜒𝜑))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wb 104
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  rbaibr  875  pm5.44  878  exmoeu2  2008  r19.9rmv  3401  dfopg  3650  brinxp  4545  elioo5  9557  prmind2  11594
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