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Theorem simp323 1317
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 1200 . 2 ((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) → 𝜒)
213ad2ant3 1127 1 ((𝜂𝜁 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1079
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 208  df-an 397  df-3an 1081
This theorem is referenced by:  dalemrot  36673  dath2  36753  cdleme18d  37311  cdleme20i  37333  cdleme20j  37334  cdleme20l2  37337  cdleme20l  37338  cdleme20m  37339  cdleme20  37340  cdleme21j  37352  cdleme22eALTN  37361  cdleme26eALTN  37377  cdlemk16a  37872  cdlemk12u-2N  37906  cdlemk21-2N  37907  cdlemk22  37909  cdlemk31  37912  cdlemk11ta  37945
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