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Theorem simp323 1324
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 1207 . 2 ((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) → 𝜒)
213ad2ant3 1134 1 ((𝜂𝜁 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1086
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 1088
This theorem is referenced by:  dalemrot  37925  dath2  38005  cdleme18d  38563  cdleme20i  38585  cdleme20j  38586  cdleme20l2  38589  cdleme20l  38590  cdleme20m  38591  cdleme20  38592  cdleme21j  38604  cdleme22eALTN  38613  cdleme26eALTN  38629  cdlemk16a  39124  cdlemk12u-2N  39158  cdlemk21-2N  39159  cdlemk22  39161  cdlemk31  39164  cdlemk11ta  39197
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