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Theorem simp323 1425
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 1266 . 2 ((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) → 𝜒)
213ad2ant3 1166 1 ((𝜂𝜁 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1108
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 199  df-an 386  df-3an 1110
This theorem is referenced by:  dalemrot  35678  dath2  35758  cdleme18d  36316  cdleme20i  36338  cdleme20j  36339  cdleme20l2  36342  cdleme20l  36343  cdleme20m  36344  cdleme20  36345  cdleme21j  36357  cdleme22eALTN  36366  cdleme26eALTN  36382  cdlemk16a  36877  cdlemk12u-2N  36911  cdlemk21-2N  36912  cdlemk22  36914  cdlemk31  36917  cdlemk11ta  36950
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