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Theorem simp322 1204
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 1087 . 2 ((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) → 𝜓)
213ad2ant3 1076 1 ((𝜂𝜁 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜓)
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:  dalemqnet  33759  dalemrot  33764  dath2  33844  cdleme18d  34403  cdleme20i  34426  cdleme20j  34427  cdleme20l2  34430  cdleme20l  34431  cdleme20m  34432  cdleme20  34433  cdleme21j  34445  cdleme22eALTN  34454  cdleme26eALTN  34470  cdlemk16a  34965  cdlemk12u-2N  34999  cdlemk21-2N  35000  cdlemk22  35002  cdlemk31  35005  cdlemk32  35006  cdlemk11ta  35038  cdlemk11tc  35054
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