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Theorem simp3r3 1275
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 1188 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜒)
213ad2ant3 1127 1 ((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  w3a 1079
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 208  df-an 397  df-3an 1081
This theorem is referenced by:  nllyrest  22022  cdlemblem  36809  cdleme21  37353  cdleme22b  37357  cdleme40m  37483  cdlemg34  37728  cdlemk5u  37877  cdlemk6u  37878  cdlemk21N  37889  cdlemk20  37890  cdlemk26b-3  37921  cdlemk26-3  37922  cdlemk28-3  37924  cdlemky  37942  cdlemk11t  37962  cdlemkyyN  37978  dihmeetlem20N  38342  stoweidlem56  42218
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