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Theorem nulel0c 4422
 Description: The empty set is a member of cardinal zero. (Contributed by SF, 13-Feb-2015.)
Assertion
Ref Expression
nulel0c 0c

Proof of Theorem nulel0c
StepHypRef Expression
1 eqid 2353 . 2
2 el0c 4421 . 2 0c
31, 2mpbir 200 1 0c
 Colors of variables: wff setvar class Syntax hints:   wceq 1642   wcel 1710  c0 3550  0cc0c 4374 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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 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-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 This theorem is referenced by:  ncfinraise  4481  ncfinlower  4483  tfin0c  4497  nulnnn  4556  tc0c  6163  ce0nnul  6177  ce0nn  6180  ce0nulnc  6184
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