Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  nn0xnn0 GIF version

Theorem nn0xnn0 9064
 Description: A standard nonnegative integer is an extended nonnegative integer. (Contributed by AV, 10-Dec-2020.)
Assertion
Ref Expression
nn0xnn0 (𝐴 ∈ ℕ0𝐴 ∈ ℕ0*)

Proof of Theorem nn0xnn0
StepHypRef Expression
1 nn0ssxnn0 9063 . 2 0 ⊆ ℕ0*
21sseli 3094 1 (𝐴 ∈ ℕ0𝐴 ∈ ℕ0*)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∈ wcel 1481  ℕ0cn0 8997  ℕ0*cxnn0 9060 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2689  df-un 3076  df-in 3078  df-ss 3085  df-xnn0 9061 This theorem is referenced by:  xnn0xadd0  9676  1tonninf  10240
 Copyright terms: Public domain W3C validator