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Theorem simp323 1205
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 1088 . 2 ((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) → 𝜒)
213ad2ant3 1076 1 ((𝜂𝜁 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1030
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 195  df-an 384  df-3an 1032
This theorem is referenced by:  dalemrot  33760  dath2  33840  cdleme18d  34399  cdleme20i  34422  cdleme20j  34423  cdleme20l2  34426  cdleme20l  34427  cdleme20m  34428  cdleme20  34429  cdleme21j  34441  cdleme22eALTN  34450  cdleme26eALTN  34466  cdlemk16a  34961  cdlemk12u-2N  34995  cdlemk21-2N  34996  cdlemk22  34998  cdlemk31  35001  cdlemk11ta  35034
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