Theorem nn0ssxnn0 12477

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 4130	. 2 ⊢ ℕ0 ⊆ (ℕ0 ∪ {+∞})
2		df-xnn0 12475	. 2 ⊢ ℕ0* = (ℕ0 ∪ {+∞})
3	1, 2	sseqtrri 3983	1 ⊢ ℕ0 ⊆ ℕ0*

Syntax hints:   ∪ cun 3899   ⊆ wss 3901  {csn 4580  +∞cpnf 11163  ℕ₀cn0 12401  ℕ₀^*cxnn0 12474

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2715  df-cleq 2728  df-clel 2811  df-v 3442  df-un 3906  df-ss 3918  df-xnn0 12475

This theorem is referenced by:  nn0xnn0  12478  0xnn0  12480  nn0xnn0d  12483