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Theorem simp311 1420
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 1261 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜑)
213ad2ant3 1166 1 ((𝜂𝜁 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1108
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 199  df-an 386  df-3an 1110
This theorem is referenced by:  dalem-clpjq  35658  dath2  35758  cdleme26e  36380  cdleme38m  36484  cdleme38n  36485  cdleme39n  36487  cdlemg28b  36724  cdlemk7  36869  cdlemk11  36870  cdlemk12  36871  cdlemk7u  36891  cdlemk11u  36892  cdlemk12u  36893  cdlemk22  36914  cdlemk23-3  36923  cdlemk25-3  36925
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