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Theorem simp331 1322
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp331 ((𝜂𝜁 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒))) → 𝜑)

Proof of Theorem simp331
StepHypRef Expression
1 simp31 1205 . 2 ((𝜃𝜏 ∧ (𝜑𝜓𝜒)) → 𝜑)
213ad2ant3 1131 1 ((𝜂𝜁 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒))) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1083
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 209  df-an 399  df-3an 1085
This theorem is referenced by:  ivthALT  33687  dalemclpjs  36774  dath2  36877  cdlema1N  36931  cdlemk7u  38010  cdlemk11u  38011  cdlemk12u  38012  cdlemk22  38033  cdlemk23-3  38042  cdlemk24-3  38043  cdlemk33N  38049  cdlemk11ta  38069  cdlemk11tc  38085  cdlemk54  38098
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