Theorem nn0ssxnn0 12593

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 4170	. 2 ⊢ ℕ0 ⊆ (ℕ0 ∪ {+∞})
2		df-xnn0 12591	. 2 ⊢ ℕ0* = (ℕ0 ∪ {+∞})
3	1, 2	sseqtrri 4016	1 ⊢ ℕ0 ⊆ ℕ0*

Syntax hints:   ∪ cun 3944   ⊆ wss 3946  {csn 4623  +∞cpnf 11286  ℕ₀cn0 12518  ℕ₀^*cxnn0 12590

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2697

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2704  df-cleq 2718  df-clel 2803  df-v 3464  df-un 3951  df-ss 3963  df-xnn0 12591

This theorem is referenced by:  nn0xnn0  12594  0xnn0  12596  nn0xnn0d  12599