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Theorem baib 862
Description: Move conjunction outside of biconditional. (Contributed by NM, 13-May-1999.)
Hypothesis
Ref Expression
baib.1 (𝜑 ↔ (𝜓𝜒))
Assertion
Ref Expression
baib (𝜓 → (𝜑𝜒))

Proof of Theorem baib
StepHypRef Expression
1 ibar 295 . 2 (𝜓 → (𝜒 ↔ (𝜓𝜒)))
2 baib.1 . 2 (𝜑 ↔ (𝜓𝜒))
31, 2syl6rbbr 197 1 (𝜓 → (𝜑𝜒))
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:  baibr  863  rbaib  864  ceqsrexbv  2736  elrab3  2760  rabsn  3483  elrint2  3703  frind  4142  fnres  5081  f1ompt  5393  fliftfun  5513  ovid  5694  brdifun  6247  xpcomco  6470  ltexprlemdisj  7066  xrlenlt  7452  reapval  7951  znnnlt1  8692  difrp  9063  elfz  9323  fzolb2  9452  elfzo3  9461  fzouzsplit  9477  rpexp  10910
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