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Theorem simp3r1 1281
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 1194 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜑)
213ad2ant3 1135 1 ((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  w3a 1087
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 206  df-an 397  df-3an 1089
This theorem is referenced by:  nllyrest  22821  segletr  34666  cdlemblem  38223  cdleme21  38767  cdleme22b  38771  cdleme40m  38897  cdlemg34  39142  cdlemk5u  39291  cdlemk6u  39292  cdlemk21N  39303  cdlemk20  39304  cdlemk26b-3  39335  cdlemk26-3  39336  cdlemk28-3  39338  cdlemk37  39344  cdlemky  39356  cdlemk11t  39376  cdlemkyyN  39392  dihmeetlem20N  39756  stoweidlem56  44229
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