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Theorem simp3bi 956
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
simp3bi (𝜑𝜃)

Proof of Theorem simp3bi
StepHypRef Expression
1 3simp1bi.1 . . 3 (𝜑 ↔ (𝜓𝜒𝜃))
21biimpi 118 . 2 (𝜑 → (𝜓𝜒𝜃))
32simp3d 953 1 (𝜑𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 103  w3a 920
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  df-3an 922
This theorem is referenced by:  limuni  4180  smores2  5965  ersym  6207  ertr  6210  eluzle  8789
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