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Theorem simp322 1232
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 1115 . 2 ((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) → 𝜓)
213ad2ant3 1104 1 ((𝜂𝜁 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1054
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 197  df-an 385  df-3an 1056
This theorem is referenced by:  dalemqnet  35256  dalemrot  35261  dath2  35341  cdleme18d  35900  cdleme20i  35922  cdleme20j  35923  cdleme20l2  35926  cdleme20l  35927  cdleme20m  35928  cdleme20  35929  cdleme21j  35941  cdleme22eALTN  35950  cdleme26eALTN  35966  cdlemk16a  36461  cdlemk12u-2N  36495  cdlemk21-2N  36496  cdlemk22  36498  cdlemk31  36501  cdlemk32  36502  cdlemk11ta  36534  cdlemk11tc  36550
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