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Theorem simp321 1323
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 1206 . 2 ((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) → 𝜑)
213ad2ant3 1135 1 ((𝜂𝜁 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜑)
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 206  df-an 397  df-3an 1089
This theorem is referenced by:  dalemcnes  38324  dalempnes  38325  dalemrot  38331  dath2  38411  cdleme18d  38969  cdleme20i  38991  cdleme20j  38992  cdleme20l2  38995  cdleme20l  38996  cdleme20m  38997  cdleme20  38998  cdleme21j  39010  cdleme22eALTN  39019  cdlemk16a  39530  cdlemk12u-2N  39564  cdlemk21-2N  39565  cdlemk22  39567  cdlemk31  39570  cdlemk32  39571  cdlemk11ta  39603  cdlemk11tc  39619
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