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Theorem simp212 1311
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 1203 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜓)
213ad2ant2 1133 1 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜁) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1086
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 397  df-3an 1088
This theorem is referenced by:  cdleme27a  38643  cdlemk5u  39137  cdlemk6u  39138  cdlemk7u  39146  cdlemk11u  39147  cdlemk12u  39148  cdlemk7u-2N  39164  cdlemk11u-2N  39165  cdlemk12u-2N  39166  cdlemk20-2N  39168  cdlemk22  39169  cdlemk22-3  39177  cdlemk33N  39185  cdlemk53b  39232  cdlemk53  39233  cdlemk55a  39235  cdlemkyyN  39238  cdlemk43N  39239
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