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Theorem simp311 1319
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 1202 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜑)
213ad2ant3 1134 1 ((𝜂𝜁 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1086
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 206  df-an 397  df-3an 1088
This theorem is referenced by:  dalem-clpjq  37651  dath2  37751  cdleme26e  38373  cdleme38m  38477  cdleme38n  38478  cdleme39n  38480  cdlemg28b  38717  cdlemk7  38862  cdlemk11  38863  cdlemk12  38864  cdlemk7u  38884  cdlemk11u  38885  cdlemk12u  38886  cdlemk22  38907  cdlemk23-3  38916  cdlemk25-3  38918
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