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Theorem simp321 1204
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp321 ((𝜂𝜁 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜑)

Proof of Theorem simp321
StepHypRef Expression
1 simp21 1087 . 2 ((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) → 𝜑)
213ad2ant3 1077 1 ((𝜂𝜁 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜑)
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:  dalemcnes  33748  dalempnes  33749  dalemrot  33755  dath2  33835  cdleme18d  34394  cdleme20i  34417  cdleme20j  34418  cdleme20l2  34421  cdleme20l  34422  cdleme20m  34423  cdleme20  34424  cdleme21j  34436  cdleme22eALTN  34445  cdlemk16a  34956  cdlemk12u-2N  34990  cdlemk21-2N  34991  cdlemk22  34993  cdlemk31  34996  cdlemk32  34997  cdlemk11ta  35029  cdlemk11tc  35045
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