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Theorem simp23 1027
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 994 . 2 ((𝜓𝜒𝜃) → 𝜃)
213ad2ant2 1014 1 ((𝜑 ∧ (𝜓𝜒𝜃) ∧ 𝜏) → 𝜃)
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:  simpl23  1072  simpr23  1081  simp123  1126  simp223  1135  simp323  1144  funtpg  5249
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