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

Theorem simp3l3 1166
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 1064 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜒)
213ad2ant3 1082 1 ((𝜏𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  w3a 1036
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 386  df-3an 1038
This theorem is referenced by:  cvmlift2lem10  31002  noprefixmo  31573  cdleme36m  35229  cdlemk5u  35629  cdlemk21N  35641  cdlemk20  35642  cdlemk27-3  35675  cdlemk28-3  35676  dihmeetlem20N  36095
  Copyright terms: Public domain W3C validator