Theorem 0xnn0 9586

Description: Zero is an extended nonnegative integer. (Contributed by AV, 10-Dec-2020.)

Assertion

Ref	Expression
0xnn0	⊢ 0 ∈ ℕ0*

Proof of Theorem 0xnn0

Step	Hyp	Ref	Expression
1		nn0ssxnn0 9583	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 9528	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3239	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 2205  0cc0 8143  ℕ₀cn0 9513  ℕ₀^*cxnn0 9580

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2216  ax-1cn 8236  ax-icn 8238  ax-addcl 8239  ax-mulcl 8241  ax-i2m1 8248

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-nfc 2375  df-v 2817  df-un 3218  df-in 3220  df-ss 3227  df-sn 3700  df-n0 9514  df-xnn0 9581

This theorem is referenced by:  0tonninf  10826