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Theorem simp232 1318
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 1210 . 2 ((𝜃𝜏 ∧ (𝜑𝜓𝜒)) → 𝜓)
213ad2ant2 1134 1 ((𝜂 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒)) ∧ 𝜁) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1087
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 206  df-an 397  df-3an 1089
This theorem is referenced by:  cdlemd3  38654  cdleme21ct  38783  cdleme21e  38785  cdleme21f  38786  cdleme21i  38789  cdleme26eALTN  38815  cdlemk23-3  39356  cdlemk25-3  39358
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