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Theorem simp212 1198
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 1090 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜓)
213ad2ant2 1081 1 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜁) → 𝜓)
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  35170  cdlemk5u  35664  cdlemk6u  35665  cdlemk7u  35673  cdlemk11u  35674  cdlemk12u  35675  cdlemk7u-2N  35691  cdlemk11u-2N  35692  cdlemk12u-2N  35693  cdlemk20-2N  35695  cdlemk22  35696  cdlemk22-3  35704  cdlemk33N  35712  cdlemk53b  35759  cdlemk53  35760  cdlemk55a  35762  cdlemkyyN  35765  cdlemk43N  35766
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