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Theorem simp1bi 919
Description: Deduce a conjunct from a triple conjunction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypothesis
Ref Expression
3simp1bi.1 (𝜑 ↔ (𝜓𝜒𝜃))
Assertion
Ref Expression
simp1bi (𝜑𝜓)

Proof of Theorem simp1bi
StepHypRef Expression
1 3simp1bi.1 . . 3 (𝜑 ↔ (𝜓𝜒𝜃))
21biimpi 113 . 2 (𝜑 → (𝜓𝜒𝜃))
32simp1d 916 1 (𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  w3a 885
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99
This theorem depends on definitions:  df-bi 110  df-3an 887
This theorem is referenced by:  limord  4128  smores2  5896  smofvon2dm  5898  smofvon  5901  errel  6102  lincmb01cmp  8838  iccf1o  8839  elfznn0  8942  elfzouz  8975
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