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Theorem simp311 1381
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 1222 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜑)
213ad2ant3 1127 1 ((𝜂𝜁 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜑)
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:  dalem-clpjq  35395  dath2  35495  cdleme26e  36118  cdleme38m  36222  cdleme38n  36223  cdleme39n  36225  cdlemg28b  36462  cdlemk7  36607  cdlemk11  36608  cdlemk12  36609  cdlemk7u  36629  cdlemk11u  36630  cdlemk12u  36631  cdlemk22  36652  cdlemk23-3  36661  cdlemk25-3  36663
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