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Theorem simp313 1202
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 1085 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜒)
213ad2ant3 1076 1 ((𝜂𝜁 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1030
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 195  df-an 384  df-3an 1032
This theorem is referenced by:  dalemrot  33764  dalem5  33774  dalem-cly  33778  dath2  33844  cdleme26e  34468  cdleme38m  34572  cdleme38n  34573  cdlemg28b  34812  cdlemg28  34813  cdlemk7  34957  cdlemk11  34958  cdlemk12  34959  cdlemk7u  34979  cdlemk11u  34980  cdlemk12u  34981  cdlemk22  35002  cdlemk23-3  35011  cdlemk25-3  35013
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