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Theorem simp313 1407
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp313 ((𝜂𝜁 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜒)

Proof of Theorem simp313
StepHypRef Expression
1 simp13 1248 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜒)
213ad2ant3 1130 1 ((𝜂𝜁 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1072
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 385  df-3an 1074
This theorem is referenced by:  dalemrot  35446  dalem5  35456  dalem-cly  35460  dath2  35526  cdleme26e  36149  cdleme38m  36253  cdleme38n  36254  cdlemg28b  36493  cdlemg28  36494  cdlemk7  36638  cdlemk11  36639  cdlemk12  36640  cdlemk7u  36660  cdlemk11u  36661  cdlemk12u  36662  cdlemk22  36683  cdlemk23-3  36692  cdlemk25-3  36694
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