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Theorem simp212 1193
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 1085 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜓)
213ad2ant2 1076 1 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜁) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1031
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 196  df-an 385  df-3an 1033
This theorem is referenced by:  cdleme27a  34673  cdlemk5u  35167  cdlemk6u  35168  cdlemk7u  35176  cdlemk11u  35177  cdlemk12u  35178  cdlemk7u-2N  35194  cdlemk11u-2N  35195  cdlemk12u-2N  35196  cdlemk20-2N  35198  cdlemk22  35199  cdlemk22-3  35207  cdlemk33N  35215  cdlemk53b  35262  cdlemk53  35263  cdlemk55a  35265  cdlemkyyN  35268  cdlemk43N  35269
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