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Theorem simp12 1030
Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
Assertion
Ref Expression
simp12 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜓)

Proof of Theorem simp12
StepHypRef Expression
1 simp2 1000 . 2 ((𝜑𝜓𝜒) → 𝜓)
213ad2ant1 1020 1 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 980
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 982
This theorem is referenced by:  simpl12  1075  simpr12  1084  simp112  1129  simp212  1138  simp312  1147  frecsuclem  6432  dvdsgcd  12048  coprimeprodsq  12292  pythagtriplem4  12303  pythagtriplem13  12311  pythagtriplem14  12312  pythagtriplem16  12314  pythagtrip  12318  pceu  12330
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