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Theorem simp322 1324
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 1207 . 2 ((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) → 𝜓)
213ad2ant3 1135 1 ((𝜂𝜁 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1087
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 206  df-an 397  df-3an 1089
This theorem is referenced by:  dalemqnet  38047  dalemrot  38052  dath2  38132  cdleme18d  38690  cdleme20i  38712  cdleme20j  38713  cdleme20l2  38716  cdleme20l  38717  cdleme20m  38718  cdleme20  38719  cdleme21j  38731  cdleme22eALTN  38740  cdleme26eALTN  38756  cdlemk16a  39251  cdlemk12u-2N  39285  cdlemk21-2N  39286  cdlemk22  39288  cdlemk31  39291  cdlemk32  39292  cdlemk11ta  39324  cdlemk11tc  39340
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