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Theorem simp311 1206
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 1089 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜑)
213ad2ant3 1082 1 ((𝜂𝜁 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1036
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 386  df-3an 1038
This theorem is referenced by:  dalem-clpjq  34389  dath2  34489  cdleme26e  35113  cdleme38m  35217  cdleme38n  35218  cdleme39n  35220  cdlemg28b  35457  cdlemk7  35602  cdlemk11  35603  cdlemk12  35604  cdlemk7u  35624  cdlemk11u  35625  cdlemk12u  35626  cdlemk22  35647  cdlemk23-3  35656  cdlemk25-3  35658
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