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Theorem simp22 973
Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
Assertion
Ref Expression
simp22 ((𝜑 ∧ (𝜓𝜒𝜃) ∧ 𝜏) → 𝜒)

Proof of Theorem simp22
StepHypRef Expression
1 simp2 940 . 2 ((𝜓𝜒𝜃) → 𝜒)
213ad2ant2 961 1 ((𝜑 ∧ (𝜓𝜒𝜃) ∧ 𝜏) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 922
This theorem is referenced by:  simpl22  1018  simpr22  1027  simp122  1072  simp222  1081  simp322  1090  prarloclem5  6962
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