Theorem rabnc 3809

Description: Law of noncontradiction, in terms of restricted class abstractions. (Contributed by Jeff Madsen, 20-Jun-2011.)

Assertion

Ref	Expression
rabnc

Distinct variable group:   ,

Proof of Theorem rabnc

Step	Hyp	Ref	Expression
1		inrab 3769	. 2
2		rabeq0 3807	. . 3
3		pm3.24 882	. . . 4
4	3	a1i 11	. . 3
5	2, 4	mprgbir 2821	. 2
6	1, 5	eqtri 2486	1

Syntax hints:  -.wn 3  /\wa 369  =wceq 1395  e.wcel 1818  {crab 2811  i^icin 3474  c0 3784

This theorem is referenced by:  hasheuni  28091  ddemeas  28208  ballotth  28476  jm2.22  30937

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-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-in 3482  df-nul 3785