MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  simp3l3 Structured version   Visualization version   GIF version

Theorem simp3l3 1279
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp3l3 ((𝜏𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜒)

Proof of Theorem simp3l3
StepHypRef Expression
1 simpl3 1192 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜒)
213ad2ant3 1134 1 ((𝜏𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 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:  cvmlift2lem10  35297  cdleme36m  40444  cdlemk5u  40844  cdlemk21N  40856  cdlemk20  40857  cdlemk27-3  40890  cdlemk28-3  40891  dihmeetlem20N  41309
  Copyright terms: Public domain W3C validator