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Theorem simp3r3 1383
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp3r3 ((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜒)

Proof of Theorem simp3r3
StepHypRef Expression
1 simpr3 1253 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜒)
213ad2ant3 1166 1 ((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 385  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:  nllyrest  21618  cdlemblem  35814  cdleme21  36358  cdleme22b  36362  cdleme40m  36488  cdlemg34  36733  cdlemk5u  36882  cdlemk6u  36883  cdlemk21N  36894  cdlemk20  36895  cdlemk26b-3  36926  cdlemk26-3  36927  cdlemk28-3  36929  cdlemky  36947  cdlemk11t  36967  cdlemkyyN  36983  dihmeetlem20N  37347  stoweidlem56  41012
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