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Theorem simp233 1404
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp233 ((𝜂 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒)) ∧ 𝜁) → 𝜒)

Proof of Theorem simp233
StepHypRef Expression
1 simp33 1254 . 2 ((𝜃𝜏 ∧ (𝜑𝜓𝜒)) → 𝜒)
213ad2ant2 1129 1 ((𝜂 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒)) ∧ 𝜁) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1072
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-an 385  df-3an 1074
This theorem is referenced by:  cdlemd3  35990  cdleme21ct  36119  cdleme21e  36121  cdleme26eALTN  36151  cdlemk23-3  36692
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