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Theorem simp3r1 1278
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp3r1 ((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜑)

Proof of Theorem simp3r1
StepHypRef Expression
1 simpr1 1191 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜑)
213ad2ant3 1132 1 ((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399  w3a 1084
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 1086
This theorem is referenced by:  nllyrest  22094  segletr  33683  cdlemblem  37082  cdleme21  37626  cdleme22b  37630  cdleme40m  37756  cdlemg34  38001  cdlemk5u  38150  cdlemk6u  38151  cdlemk21N  38162  cdlemk20  38163  cdlemk26b-3  38194  cdlemk26-3  38195  cdlemk28-3  38197  cdlemk37  38203  cdlemky  38215  cdlemk11t  38235  cdlemkyyN  38251  dihmeetlem20N  38615  stoweidlem56  42685
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