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Theorem simp331 1207
 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 1090 . 2 ((𝜃𝜏 ∧ (𝜑𝜓𝜒)) → 𝜑)
213ad2ant3 1077 1 ((𝜂𝜁 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒))) → 𝜑)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ w3a 1031 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 196  df-an 385  df-3an 1033 This theorem is referenced by:  ivthALT  31500  dalemclpjs  33938  dath2  34041  cdlema1N  34095  cdlemk7u  35176  cdlemk11u  35177  cdlemk12u  35178  cdlemk22  35199  cdlemk23-3  35208  cdlemk24-3  35209  cdlemk33N  35215  cdlemk11ta  35235  cdlemk11tc  35251  cdlemk54  35264
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