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Theorem simp22 949
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 916 . 2 ((𝜓𝜒𝜃) → 𝜒)
213ad2ant2 937 1 ((𝜑 ∧ (𝜓𝜒𝜃) ∧ 𝜏) → 𝜒)
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:  simpl22  994  simpr22  1003  simp122  1048  simp222  1057  simp322  1066  prarloclem5  6655
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