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Theorem simp3r3 1169
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 1067 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜒)
213ad2ant3 1082 1 ((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  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:  nllyrest  21199  noprefixmo  31573  cdlemblem  34559  cdleme21  35105  cdleme22b  35109  cdleme40m  35235  cdlemg34  35480  cdlemk5u  35629  cdlemk6u  35630  cdlemk21N  35641  cdlemk20  35642  cdlemk26b-3  35673  cdlemk26-3  35674  cdlemk28-3  35676  cdlemky  35694  cdlemk11t  35714  cdlemkyyN  35730  dihmeetlem20N  36095  stoweidlem56  39580
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