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Theorem simp11 1012
Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
Assertion
Ref Expression
simp11 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜑)

Proof of Theorem simp11
StepHypRef Expression
1 simp1 982 . 2 ((𝜑𝜓𝜒) → 𝜑)
213ad2ant1 1003 1 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 963
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 965
This theorem is referenced by:  simpl11  1057  simpr11  1066  simp111  1111  simp211  1120  simp311  1129  frecsuclem  6355  coprimeprodsq  12147  pythagtriplem14  12167  pythagtrip  12173
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