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Theorem simp331 1212
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 1095 . 2 ((𝜃𝜏 ∧ (𝜑𝜓𝜒)) → 𝜑)
213ad2ant3 1082 1 ((𝜂𝜁 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒))) → 𝜑)
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:  ivthALT  32007  dalemclpjs  34435  dath2  34538  cdlema1N  34592  cdlemk7u  35673  cdlemk11u  35674  cdlemk12u  35675  cdlemk22  35696  cdlemk23-3  35705  cdlemk24-3  35706  cdlemk33N  35712  cdlemk11ta  35732  cdlemk11tc  35748  cdlemk54  35761
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