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Theorem simp322 1321
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 1204 . 2 ((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) → 𝜓)
213ad2ant3 1132 1 ((𝜂𝜁 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1084
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 210  df-an 400  df-3an 1086
This theorem is referenced by:  dalemqnet  36948  dalemrot  36953  dath2  37033  cdleme18d  37591  cdleme20i  37613  cdleme20j  37614  cdleme20l2  37617  cdleme20l  37618  cdleme20m  37619  cdleme20  37620  cdleme21j  37632  cdleme22eALTN  37641  cdleme26eALTN  37657  cdlemk16a  38152  cdlemk12u-2N  38186  cdlemk21-2N  38187  cdlemk22  38189  cdlemk31  38192  cdlemk32  38193  cdlemk11ta  38225  cdlemk11tc  38241
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