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Theorem simp3r3 1282
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 1195 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜒)
213ad2ant3 1134 1 ((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  w3a 1086
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 1088
This theorem is referenced by:  nllyrest  22637  cdlemblem  37807  cdleme21  38351  cdleme22b  38355  cdleme40m  38481  cdlemg34  38726  cdlemk5u  38875  cdlemk6u  38876  cdlemk21N  38887  cdlemk20  38888  cdlemk26b-3  38919  cdlemk26-3  38920  cdlemk28-3  38922  cdlemky  38940  cdlemk11t  38960  cdlemkyyN  38976  dihmeetlem20N  39340  stoweidlem56  43597
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