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Theorem simp223 1400
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp223 ((𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) ∧ 𝜁) → 𝜒)

Proof of Theorem simp223
StepHypRef Expression
1 simp23 1250 . 2 ((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) → 𝜒)
213ad2ant2 1128 1 ((𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) ∧ 𝜁) → 𝜒)
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:  4atexlemswapqr  35864  4atexlemcnd  35873  cdleme26eALTN  36163  cdleme27a  36169  cdlemk23-3  36704  cdlemk25-3  36706  cdlemk27-3  36709
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