Theorem nn0ssxnn0 11243

Description: The standard nonnegative integers are a subset of the extended nonnegative integers. (Contributed by AV, 10-Dec-2020.)

Assertion

Ref	Expression
nn0ssxnn0	⊢ ℕ0 ⊆ ℕ0*

Proof of Theorem nn0ssxnn0

Step	Hyp	Ref	Expression
1		ssun1 3738	. 2 ⊢ ℕ0 ⊆ (ℕ0 ∪ {+∞})
2		df-xnn0 11241	. 2 ⊢ ℕ0* = (ℕ0 ∪ {+∞})
3	1, 2	sseqtr4i 3601	1 ⊢ ℕ0 ⊆ ℕ0*

Syntax hints:   ∪ cun 3538   ⊆ wss 3540  {csn 4125  +∞cpnf 9950  ℕ₀cn0 11169  ℕ₀^*cxnn0 11240

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-un 3545  df-in 3547  df-ss 3554  df-xnn0 11241

This theorem is referenced by:  nn0xnn0  11244  0xnn0  11246  nn0xnn0d  11249