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Theorem simp2bi 931
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
simp2bi (𝜑𝜒)

Proof of Theorem simp2bi
StepHypRef Expression
1 3simp1bi.1 . . 3 (𝜑 ↔ (𝜓𝜒𝜃))
21biimpi 117 . 2 (𝜑 → (𝜓𝜒𝜃))
32simp2d 928 1 (𝜑𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 102  w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  0ellim  4163  smodm  5937  erdm  6147  dif1en  6368  eluzelz  8578  elfz3nn0  9078
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