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Theorem simp213 1199
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp213 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜁) → 𝜒)

Proof of Theorem simp213
StepHypRef Expression
1 simp13 1091 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜒)
213ad2ant2 1081 1 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜁) → 𝜒)
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:  cdleme27a  35174  cdlemk5u  35668  cdlemk6u  35669  cdlemk7u  35677  cdlemk11u  35678  cdlemk12u  35679  cdlemk7u-2N  35695  cdlemk11u-2N  35696  cdlemk12u-2N  35697  cdlemk20-2N  35699  cdlemk22  35700  cdlemk22-3  35708  cdlemk33N  35716  cdlemk53b  35763  cdlemk53  35764  cdlemk55a  35766  cdlemkyyN  35769  cdlemk43N  35770
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