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Theorem simp212 1313
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 1205 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜓)
213ad2ant2 1135 1 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜁) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1087
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 207  df-an 396  df-3an 1089
This theorem is referenced by:  cdleme27a  40369  cdlemk5u  40863  cdlemk6u  40864  cdlemk7u  40872  cdlemk11u  40873  cdlemk12u  40874  cdlemk7u-2N  40890  cdlemk11u-2N  40891  cdlemk12u-2N  40892  cdlemk20-2N  40894  cdlemk22  40895  cdlemk22-3  40903  cdlemk33N  40911  cdlemk53b  40958  cdlemk53  40959  cdlemk55a  40961  cdlemkyyN  40964  cdlemk43N  40965
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