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Theorem simp322 1205
 Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp322 ((𝜂𝜁 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜓)

Proof of Theorem simp322
StepHypRef Expression
1 simp22 1088 . 2 ((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) → 𝜓)
213ad2ant3 1077 1 ((𝜂𝜁 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ w3a 1031 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 196  df-an 385  df-3an 1033 This theorem is referenced by:  dalemqnet  33956  dalemrot  33961  dath2  34041  cdleme18d  34600  cdleme20i  34623  cdleme20j  34624  cdleme20l2  34627  cdleme20l  34628  cdleme20m  34629  cdleme20  34630  cdleme21j  34642  cdleme22eALTN  34651  cdleme26eALTN  34667  cdlemk16a  35162  cdlemk12u-2N  35196  cdlemk21-2N  35197  cdlemk22  35199  cdlemk31  35202  cdlemk32  35203  cdlemk11ta  35235  cdlemk11tc  35251
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