Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  dedth3v Unicode version

Theorem dedth3v 3998
 Description: Weak deduction theorem for eliminating a hypothesis with 3 class variables. See comments in dedth2v 3997. (Contributed by NM, 13-Aug-1999.) (Proof shortened by Eric Schmidt, 28-Jul-2009.)
Hypotheses
Ref Expression
dedth3v.1
dedth3v.2
dedth3v.3
dedth3v.4
Assertion
Ref Expression
dedth3v

Proof of Theorem dedth3v
StepHypRef Expression
1 dedth3v.1 . . . 4
2 dedth3v.2 . . . 4
3 dedth3v.3 . . . 4
4 dedth3v.4 . . . 4
51, 2, 3, 4dedth3h 3995 . . 3
653anidm12 1285 . 2
76anidms 645 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  ifcif 3941 This theorem is referenced by:  sseliALT  4583 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-if 3942
 Copyright terms: Public domain W3C validator