Theorem 0xnn0 9379

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 9376	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 9325	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3194	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 2177  0cc0 7940  ℕ₀cn0 9310  ℕ₀^*cxnn0 9373

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2188  ax-1cn 8033  ax-icn 8035  ax-addcl 8036  ax-mulcl 8038  ax-i2m1 8045

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2193  df-cleq 2199  df-clel 2202  df-nfc 2338  df-v 2775  df-un 3174  df-in 3176  df-ss 3183  df-sn 3643  df-n0 9311  df-xnn0 9374

This theorem is referenced by:  0tonninf  10602