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Theorem simp321 1408
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 1249 . 2 ((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) → 𝜑)
213ad2ant3 1130 1 ((𝜂𝜁 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1072
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 385  df-3an 1074
This theorem is referenced by:  dalemcnes  35457  dalempnes  35458  dalemrot  35464  dath2  35544  cdleme18d  36103  cdleme20i  36125  cdleme20j  36126  cdleme20l2  36129  cdleme20l  36130  cdleme20m  36131  cdleme20  36132  cdleme21j  36144  cdleme22eALTN  36153  cdlemk16a  36664  cdlemk12u-2N  36698  cdlemk21-2N  36699  cdlemk22  36701  cdlemk31  36704  cdlemk32  36705  cdlemk11ta  36737  cdlemk11tc  36753
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