Theorem naddlidd

Description: Identity law for natural addition. Deduction form. (Contributed by Scott Fenton, 30-Jul-2026)

	Ref	Expression
Hypothesis	nadd.1	⊢ ( 𝜑 → 𝐴 ∈ On )
Assertion	naddlidd	⊢ ( 𝜑 → ( ∅ +no 𝐴 ) = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		nadd.1	⊢ ( 𝜑 → 𝐴 ∈ On )
2		naddlid	⊢ ( 𝐴 ∈ On → ( ∅ +no 𝐴 ) = 𝐴 )
3	1 2	syl	⊢ ( 𝜑 → ( ∅ +no 𝐴 ) = 𝐴 )