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Theorem simp311 1201
 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 1084 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜑)
213ad2ant3 1077 1 ((𝜂𝜁 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜑)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ w3a 1031 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 196  df-an 385  df-3an 1033 This theorem is referenced by:  dalem-clpjq  33941  dath2  34041  cdleme26e  34665  cdleme38m  34769  cdleme38n  34770  cdleme39n  34772  cdlemg28b  35009  cdlemk7  35154  cdlemk11  35155  cdlemk12  35156  cdlemk7u  35176  cdlemk11u  35177  cdlemk12u  35178  cdlemk22  35199  cdlemk23-3  35208  cdlemk25-3  35210
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