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Theorem simp32 976
Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
Assertion
Ref Expression
simp32 ((𝜑𝜓 ∧ (𝜒𝜃𝜏)) → 𝜃)

Proof of Theorem simp32
StepHypRef Expression
1 simp2 940 . 2 ((𝜒𝜃𝜏) → 𝜃)
213ad2ant3 962 1 ((𝜑𝜓 ∧ (𝜒𝜃𝜏)) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  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:  simpl32  1021  simpr32  1030  simp132  1075  simp232  1084  simp332  1093
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