New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  0cex Structured version   Unicode version

Theorem 0cex 4392
 Description: Cardinal zero is a set. (Contributed by SF, 14-Jan-2015.)
Assertion
Ref Expression
0cex 0c

Proof of Theorem 0cex
StepHypRef Expression
1 df-0c 4377 . 2 0c
2 snex 4111 . 2
31, 2eqeltri 2423 1 0c
 Colors of variables: wff set class Syntax hints:   wcel 1710  cvv 2859  c0 3550  csn 3737  0cc0c 4374 This theorem is referenced by:  peano1  4402  finds  4410  ltfintri  4466  0ceven  4505  0cnelphi  4595  proj1op  4598  proj2op  4599  dfnnc3  5906  ce0nn  6201  lec0cg  6219 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334  ax-nin 4078  ax-sn 4087 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-ss 3259  df-nul 3551  df-sn 3741  df-0c 4377
 Copyright terms: Public domain W3C validator