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Theorem simp212 1309
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp212 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜁) → 𝜓)

Proof of Theorem simp212
StepHypRef Expression
1 simp12 1201 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜓)
213ad2ant2 1131 1 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜁) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1084
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 395  df-3an 1086
This theorem is referenced by:  cdleme27a  40066  cdlemk5u  40560  cdlemk6u  40561  cdlemk7u  40569  cdlemk11u  40570  cdlemk12u  40571  cdlemk7u-2N  40587  cdlemk11u-2N  40588  cdlemk12u-2N  40589  cdlemk20-2N  40591  cdlemk22  40592  cdlemk22-3  40600  cdlemk33N  40608  cdlemk53b  40655  cdlemk53  40656  cdlemk55a  40658  cdlemkyyN  40661  cdlemk43N  40662
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