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Theorem simp233 1321
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 1213 . 2 ((𝜃𝜏 ∧ (𝜑𝜓𝜒)) → 𝜒)
213ad2ant2 1136 1 ((𝜂 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒)) ∧ 𝜁) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1089
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 210  df-an 400  df-3an 1091
This theorem is referenced by:  cdlemd3  37951  cdleme21ct  38080  cdleme21e  38082  cdleme26eALTN  38112  cdlemk23-3  38653
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