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Theorem simp31 1028
Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
Assertion
Ref Expression
simp31 ((𝜑𝜓 ∧ (𝜒𝜃𝜏)) → 𝜒)

Proof of Theorem simp31
StepHypRef Expression
1 simp1 992 . 2 ((𝜒𝜃𝜏) → 𝜒)
213ad2ant3 1015 1 ((𝜑𝜓 ∧ (𝜒𝜃𝜏)) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 973
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 975
This theorem is referenced by:  simpl31  1073  simpr31  1082  simp131  1127  simp231  1136  simp331  1145
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