Theorem 0xnn0 9471

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 9468	. 2 ⊢ ℕ0 ⊆ ℕ0*
2		0nn0 9417	. 2 ⊢ 0 ∈ ℕ0
3	1, 2	sselii 3224	1 ⊢ 0 ∈ ℕ0*

Syntax hints:   ∈ wcel 2202  0cc0 8032  ℕ₀cn0 9402  ℕ₀^*cxnn0 9465

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213  ax-1cn 8125  ax-icn 8127  ax-addcl 8128  ax-mulcl 8130  ax-i2m1 8137

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-v 2804  df-un 3204  df-in 3206  df-ss 3213  df-sn 3675  df-n0 9403  df-xnn0 9466

This theorem is referenced by:  0tonninf  10703