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Theorem simpr33 1265
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
Assertion
Ref Expression
simpr33 ((𝜂 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒))) → 𝜒)

Proof of Theorem simpr33
StepHypRef Expression
1 simpr3 1196 . 2 ((𝜂 ∧ (𝜑𝜓𝜒)) → 𝜒)
213ad2antr3 1190 1 ((𝜂 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒))) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  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 207  df-an 396  df-3an 1088
This theorem is referenced by:  oppccatid  17718  subccatid  17846  fuccatid  17972  setccatid  18084  catccatid  18106  estrccatid  18131  xpccatid  18187  nllyidm  23414  utoptop  24160  cgr3tr4  35999  paddasslem9  39776  cdlemd1  40146  cdlemf2  40510  cdlemk34  40858  dihmeetlem18N  41272  dihmeetlem19N  41273  ssccatid  48933  isthincd2  49186  mndtccatid  49325
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