MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  0xnn0 Structured version   Visualization version   GIF version

Theorem 0xnn0 11329
Description: Zero is an extended nonnegative integer. (Contributed by AV, 10-Dec-2020.)
Assertion
Ref Expression
0xnn0 0 ∈ ℕ0*

Proof of Theorem 0xnn0
StepHypRef Expression
1 nn0ssxnn0 11326 . 2 0 ⊆ ℕ0*
2 0nn0 11267 . 2 0 ∈ ℕ0
31, 2sselii 3585 1 0 ∈ ℕ0*
Colors of variables: wff setvar class
Syntax hints:  wcel 1987  0cc0 9896  0cn0 11252  0*cxnn0 11323
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601  ax-1cn 9954  ax-icn 9955  ax-addcl 9956  ax-mulcl 9958  ax-i2m1 9964
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-v 3192  df-un 3565  df-in 3567  df-ss 3574  df-sn 4156  df-n0 11253  df-xnn0 11324
This theorem is referenced by:  0edg0rgr  26372  rgrusgrprc  26389  rusgrprc  26390  rgrprcx  26392
  Copyright terms: Public domain W3C validator