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Theorem simp313 1319
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 1202 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜒)
213ad2ant3 1132 1 ((𝜂𝜁 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1084
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 1086
This theorem is referenced by:  dalemrot  36901  dalem5  36911  dalem-cly  36915  dath2  36981  cdleme26e  37603  cdleme38m  37707  cdleme38n  37708  cdlemg28b  37947  cdlemg28  37948  cdlemk7  38092  cdlemk11  38093  cdlemk12  38094  cdlemk7u  38114  cdlemk11u  38115  cdlemk12u  38116  cdlemk22  38137  cdlemk23-3  38146  cdlemk25-3  38148
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