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Theorem simp323 1211
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp323 ((𝜂𝜁 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜒)

Proof of Theorem simp323
StepHypRef Expression
1 simp23 1094 . 2 ((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) → 𝜒)
213ad2ant3 1082 1 ((𝜂𝜁 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1036
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 386  df-3an 1038
This theorem is referenced by:  dalemrot  34462  dath2  34542  cdleme18d  35101  cdleme20i  35124  cdleme20j  35125  cdleme20l2  35128  cdleme20l  35129  cdleme20m  35130  cdleme20  35131  cdleme21j  35143  cdleme22eALTN  35152  cdleme26eALTN  35168  cdlemk16a  35663  cdlemk12u-2N  35697  cdlemk21-2N  35698  cdlemk22  35700  cdlemk31  35703  cdlemk11ta  35736
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