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Theorem simp311 1321
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp311 ((𝜂𝜁 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜑)

Proof of Theorem simp311
StepHypRef Expression
1 simp11 1204 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜑)
213ad2ant3 1136 1 ((𝜂𝜁 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1088
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 1090
This theorem is referenced by:  dalem-clpjq  37274  dath2  37374  cdleme26e  37996  cdleme38m  38100  cdleme38n  38101  cdleme39n  38103  cdlemg28b  38340  cdlemk7  38485  cdlemk11  38486  cdlemk12  38487  cdlemk7u  38507  cdlemk11u  38508  cdlemk12u  38509  cdlemk22  38530  cdlemk23-3  38539  cdlemk25-3  38541
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