Metamath Proof Explorer


Definition df-n0

Description: Define the set of nonnegative integers. (Contributed by Raph Levien, 10-Dec-2002)

Ref Expression
Assertion df-n0 ℕ0 = ( ℕ ∪ { 0 } )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cn0 ⊢ ℕ0
1 cn ⊢ ℕ
2 cc0 ⊢ 0
3 2 csn ⊢ { 0 }
4 1 3 cun ⊢ ( ℕ ∪ { 0 } )
5 0 4 wceq ⊢ ℕ0 = ( ℕ ∪ { 0 } )