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Theorem simp3r3 1284
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 1197 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜒)
213ad2ant3 1136 1 ((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399  w3a 1088
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 210  df-an 400  df-3an 1090
This theorem is referenced by:  nllyrest  22250  cdlemblem  37463  cdleme21  38007  cdleme22b  38011  cdleme40m  38137  cdlemg34  38382  cdlemk5u  38531  cdlemk6u  38532  cdlemk21N  38543  cdlemk20  38544  cdlemk26b-3  38575  cdlemk26-3  38576  cdlemk28-3  38578  cdlemky  38596  cdlemk11t  38616  cdlemkyyN  38632  dihmeetlem20N  38996  stoweidlem56  43180
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