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

Theorem rabnc 3652
 Description: Law of noncontradiction, in terms of restricted class abstractions. (Contributed by Jeff Madsen, 20-Jun-2011.)
Assertion
Ref Expression
rabnc
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem rabnc
StepHypRef Expression
1 inrab 3614 . 2
2 rabeq0 3650 . . 3
3 pm3.24 854 . . . 4
43a1i 11 . . 3
52, 4mprgbir 2777 . 2
61, 5eqtri 2457 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 360   wceq 1653   wcel 1726  crab 2710   cin 3320  c0 3629 This theorem is referenced by:  hasheuni  24476  ballotth  24796  jm2.22  27067 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ne 2602  df-ral 2711  df-rex 2712  df-rab 2715  df-v 2959  df-dif 3324  df-in 3328  df-nul 3630
 Copyright terms: Public domain W3C validator