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Theorem simp31 940
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 904 . 2 ((𝜒𝜃𝜏) → 𝜒)
213ad2ant3 927 1 ((𝜑𝜓 ∧ (𝜒𝜃𝜏)) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 885
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-3an 887
This theorem is referenced by:  simpl31  985  simpr31  994  simp131  1039  simp231  1048  simp331  1057
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