MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  simpr33 Structured version   Visualization version   GIF version

Theorem simpr33 1266
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 1197 . 2 ((𝜂 ∧ (𝜑𝜓𝜒)) → 𝜒)
213ad2antr3 1191 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  17686  subccatid  17814  fuccatid  17940  setccatid  18052  catccatid  18074  estrccatid  18099  xpccatid  18155  nllyidm  23382  utoptop  24128  cgr3tr4  36035  paddasslem9  39817  cdlemd1  40187  cdlemf2  40551  cdlemk34  40899  dihmeetlem18N  41313  dihmeetlem19N  41314  ssccatid  49051  isthincd2  49416  mndtccatid  49566
  Copyright terms: Public domain W3C validator