Theorem 0xnn0 11369

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 11366	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 11307	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3600	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 1990  0cc0 9936  ℕ₀cn0 11292  ℕ₀^*cxnn0 11363

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602  ax-1cn 9994  ax-icn 9995  ax-addcl 9996  ax-mulcl 9998  ax-i2m1 10004

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-un 3579  df-in 3581  df-ss 3588  df-sn 4178  df-n0 11293  df-xnn0 11364

This theorem is referenced by:  0edg0rgr  26468  rgrusgrprc  26485  rusgrprc  26486  rgrprcx  26488