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Theorem simp12 1013
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 983 . 2 ((𝜑𝜓𝜒) → 𝜓)
213ad2ant1 1003 1 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜓)
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:  simpl12  1058  simpr12  1067  simp112  1112  simp212  1121  simp312  1130  frecsuclem  6310  dvdsgcd  11734
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