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Theorem simp2bi 962
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 119 . 2 (𝜑 → (𝜓𝜒𝜃))
32simp2d 959 1 (𝜑𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 104  w3a 927
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106
This theorem depends on definitions:  df-bi 116  df-3an 929
This theorem is referenced by:  0ellim  4249  smodm  6094  erdm  6342  ixpfn  6501  dif1en  6675  eluzelz  9127  elfz3nn0  9678  ef01bndlem  11212  sin01bnd  11213  cos01bnd  11214  sin01gt0  11217
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