Theorem nn0ssxnn0 12544

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 4172	. 2 ⊢ ℕ0 ⊆ (ℕ0 ∪ {+∞})
2		df-xnn0 12542	. 2 ⊢ ℕ0* = (ℕ0 ∪ {+∞})
3	1, 2	sseqtrri 4019	1 ⊢ ℕ0 ⊆ ℕ0*

Syntax hints:   ∪ cun 3946   ⊆ wss 3948  {csn 4628  +∞cpnf 11242  ℕ₀cn0 12469  ℕ₀^*cxnn0 12541

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-un 3953  df-in 3955  df-ss 3965  df-xnn0 12542

This theorem is referenced by:  nn0xnn0  12545  0xnn0  12547  nn0xnn0d  12550