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Theorem simp23 1017
Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
Assertion
Ref Expression
simp23 ((𝜑 ∧ (𝜓𝜒𝜃) ∧ 𝜏) → 𝜃)

Proof of Theorem simp23
StepHypRef Expression
1 simp3 984 . 2 ((𝜓𝜒𝜃) → 𝜃)
213ad2ant2 1004 1 ((𝜑 ∧ (𝜓𝜒𝜃) ∧ 𝜏) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 963
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 965
This theorem is referenced by:  simpl23  1062  simpr23  1071  simp123  1116  simp223  1125  simp323  1134  funtpg  5221
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