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Theorem simp3r3 1366
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 1236 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜒)
213ad2ant3 1128 1 ((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  w3a 1070
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 383  df-3an 1072
This theorem is referenced by:  nllyrest  21509  cdlemblem  35594  cdleme21  36139  cdleme22b  36143  cdleme40m  36269  cdlemg34  36514  cdlemk5u  36663  cdlemk6u  36664  cdlemk21N  36675  cdlemk20  36676  cdlemk26b-3  36707  cdlemk26-3  36708  cdlemk28-3  36710  cdlemky  36728  cdlemk11t  36748  cdlemkyyN  36764  dihmeetlem20N  37129  stoweidlem56  40784
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