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Theorem simp232 1310
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 1202 . 2 ((𝜃𝜏 ∧ (𝜑𝜓𝜒)) → 𝜓)
213ad2ant2 1126 1 ((𝜂 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒)) ∧ 𝜁) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1079
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 208  df-an 397  df-3an 1081
This theorem is referenced by:  cdlemd3  37216  cdleme21ct  37345  cdleme21e  37347  cdleme21f  37348  cdleme21i  37351  cdleme26eALTN  37377  cdlemk23-3  37918  cdlemk25-3  37920
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