Theorem 0xnn0 9426

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 9423	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 9372	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3221	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 2200  0cc0 7987  ℕ₀cn0 9357  ℕ₀^*cxnn0 9420

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211  ax-1cn 8080  ax-icn 8082  ax-addcl 8083  ax-mulcl 8085  ax-i2m1 8092

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-v 2801  df-un 3201  df-in 3203  df-ss 3210  df-sn 3672  df-n0 9358  df-xnn0 9421

This theorem is referenced by:  0tonninf  10649