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Theorem simp323 1321
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp323 ((𝜂𝜁 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜒)

Proof of Theorem simp323
StepHypRef Expression
1 simp23 1204 . 2 ((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) → 𝜒)
213ad2ant3 1131 1 ((𝜂𝜁 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1083
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 209  df-an 399  df-3an 1085
This theorem is referenced by:  dalemrot  36797  dath2  36877  cdleme18d  37435  cdleme20i  37457  cdleme20j  37458  cdleme20l2  37461  cdleme20l  37462  cdleme20m  37463  cdleme20  37464  cdleme21j  37476  cdleme22eALTN  37485  cdleme26eALTN  37501  cdlemk16a  37996  cdlemk12u-2N  38030  cdlemk21-2N  38031  cdlemk22  38033  cdlemk31  38036  cdlemk11ta  38069
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