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Theorem simp12 946
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 916 . 2 ((𝜑𝜓𝜒) → 𝜓)
213ad2ant1 936 1 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  simpl12  991  simpr12  1000  simp112  1045  simp212  1054  simp312  1063
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