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Theorem simp211 1303
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp211 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜁) → 𝜑)

Proof of Theorem simp211
StepHypRef Expression
1 simp11 1195 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜑)
213ad2ant2 1126 1 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜁) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1079
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 208  df-an 397  df-3an 1081
This theorem is referenced by:  cdleme27a  37383  cdlemk5u  37877  cdlemk6u  37878  cdlemk7u  37886  cdlemk11u  37887  cdlemk12u  37888  cdlemk7u-2N  37904  cdlemk11u-2N  37905  cdlemk12u-2N  37906  cdlemk20-2N  37908  cdlemk22  37909  cdlemk33N  37925  cdlemk53b  37972  cdlemk53  37973  cdlemk55a  37975  cdlemkyyN  37978  cdlemk43N  37979
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