MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  simp3r3 Structured version   Visualization version   GIF version

Theorem simp3r3 1368
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 1238 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜒)
213ad2ant3 1130 1 ((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  w3a 1072
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 197  df-an 385  df-3an 1074
This theorem is referenced by:  nllyrest  21511  cdlemblem  35600  cdleme21  36145  cdleme22b  36149  cdleme40m  36275  cdlemg34  36520  cdlemk5u  36669  cdlemk6u  36670  cdlemk21N  36681  cdlemk20  36682  cdlemk26b-3  36713  cdlemk26-3  36714  cdlemk28-3  36716  cdlemky  36734  cdlemk11t  36754  cdlemkyyN  36770  dihmeetlem20N  37135  stoweidlem56  40794
  Copyright terms: Public domain W3C validator