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Theorem simp312 1317
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp312 ((𝜂𝜁 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜓)

Proof of Theorem simp312
StepHypRef Expression
1 simp12 1200 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜓)
213ad2ant3 1131 1 ((𝜂𝜁 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1083
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 209  df-an 399  df-3an 1085
This theorem is referenced by:  dalemrot  36787  dalem-cly  36801  dath2  36867  cdleme26e  37489  cdleme38m  37593  cdleme38n  37594  cdleme39n  37596  cdlemg28b  37833  cdlemk7  37978  cdlemk11  37979  cdlemk12  37980  cdlemk7u  38000  cdlemk11u  38001  cdlemk12u  38002  cdlemk22  38023  cdlemk23-3  38032  cdlemk25-3  38034
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