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Theorem simp13 971
Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
Assertion
Ref Expression
simp13 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜒)

Proof of Theorem simp13
StepHypRef Expression
1 simp3 941 . 2 ((𝜑𝜓𝜒) → 𝜒)
213ad2ant1 960 1 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜒)
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:  simpl13  1016  simpr13  1025  simp113  1070  simp213  1079  simp313  1088  funtpg  5001  dvdsgcd  10626
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