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Theorem rabnc 3791
 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 3752 . 2
2 rabeq0 3789 . . 3
3 pm3.24 880 . . . 4
43a1i 11 . . 3
52, 4mprgbir 2805 . 2
61, 5eqtri 2470 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wa 369   wceq 1381   wcel 1802  crab 2795   cin 3457  c0 3767 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1603  ax-4 1616  ax-5 1689  ax-6 1732  ax-7 1774  ax-10 1821  ax-11 1826  ax-12 1838  ax-13 1983  ax-ext 2419 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1384  df-ex 1598  df-nf 1602  df-sb 1725  df-clab 2427  df-cleq 2433  df-clel 2436  df-nfc 2591  df-ne 2638  df-ral 2796  df-rex 2797  df-rab 2800  df-v 3095  df-dif 3461  df-in 3465  df-nul 3768 This theorem is referenced by:  hasheuni  27957  ddemeas  28074  ballotth  28342  jm2.22  30905
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