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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 395  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 206  df-an 396  df-3an 1086
This theorem is referenced by:  nllyrest  23341  segletr  35619  cdlemblem  39175  cdleme21  39719  cdleme22b  39723  cdleme40m  39849  cdlemg34  40094  cdlemk5u  40243  cdlemk6u  40244  cdlemk21N  40255  cdlemk20  40256  cdlemk26b-3  40287  cdlemk26-3  40288  cdlemk28-3  40290  cdlemk37  40296  cdlemky  40308  cdlemk11t  40328  cdlemkyyN  40344  dihmeetlem20N  40708  stoweidlem56  45325
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