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Theorem simp331 1426
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 1267 . 2 ((𝜃𝜏 ∧ (𝜑𝜓𝜒)) → 𝜑)
213ad2ant3 1166 1 ((𝜂𝜁 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒))) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1108
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 199  df-an 386  df-3an 1110
This theorem is referenced by:  ivthALT  32842  dalemclpjs  35655  dath2  35758  cdlema1N  35812  cdlemk7u  36891  cdlemk11u  36892  cdlemk12u  36893  cdlemk22  36914  cdlemk23-3  36923  cdlemk24-3  36924  cdlemk33N  36930  cdlemk11ta  36950  cdlemk11tc  36966  cdlemk54  36979
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