Theorem 0xnn0 9240

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 9237	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 9186	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3152	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 2148  0cc0 7807  ℕ₀cn0 9171  ℕ₀^*cxnn0 9234

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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159  ax-1cn 7900  ax-icn 7902  ax-addcl 7903  ax-mulcl 7905  ax-i2m1 7912

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-un 3133  df-in 3135  df-ss 3142  df-sn 3598  df-n0 9172  df-xnn0 9235

This theorem is referenced by:  0tonninf  10433