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Theorem simp232 1402
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp232 ((𝜂 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒)) ∧ 𝜁) → 𝜓)

Proof of Theorem simp232
StepHypRef Expression
1 simp32 1252 . 2 ((𝜃𝜏 ∧ (𝜑𝜓𝜒)) → 𝜓)
213ad2ant2 1128 1 ((𝜂 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒)) ∧ 𝜁) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1071
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 383  df-3an 1073
This theorem is referenced by:  cdlemd3  36009  cdleme21ct  36138  cdleme21e  36140  cdleme21f  36141  cdleme21i  36144  cdleme26eALTN  36170  cdlemk23-3  36711  cdlemk25-3  36713
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