Theorem nna0

Description: Addition with zero. Theorem 4I(A1) of Enderton p. 79. (Contributed by NM, 20-Sep-1995)

	Ref	Expression
Assertion	nna0	⊢ ( 𝐴 ∈ ω → ( 𝐴 +o ∅ ) = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		nnon	⊢ ( 𝐴 ∈ ω → 𝐴 ∈ On )
2		oa0	⊢ ( 𝐴 ∈ On → ( 𝐴 +o ∅ ) = 𝐴 )
3	1 2	syl	⊢ ( 𝐴 ∈ ω → ( 𝐴 +o ∅ ) = 𝐴 )