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Theorem simp13 1029
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 999 . 2 ((𝜑𝜓𝜒) → 𝜒)
213ad2ant1 1018 1 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 978
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 980
This theorem is referenced by:  simpl13  1074  simpr13  1083  simp113  1128  simp213  1137  simp313  1146  funtpg  5262  dvdsgcd  11983  coprimeprodsq  12227  pythagtriplem4  12238  pythagtriplem13  12246  pythagtriplem14  12247  pythagtriplem16  12249  pythagtrip  12253
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