Theorem naddcld

Description: Closure law for natural addition. Deduction version. (Contributed by Scott Fenton, 10-Jun-2025)

	Ref	Expression
Hypotheses	naddcld.1	|- ( ph -> A e. On )
	naddcld.2	|- ( ph -> B e. On )
Assertion	naddcld	|- ( ph -> ( A +no B ) e. On )

Proof

Step	Hyp	Ref	Expression
1		naddcld.1	|- ( ph -> A e. On )
2		naddcld.2	|- ( ph -> B e. On )
3		naddcl	|- ( ( A e. On /\ B e. On ) -> ( A +no B ) e. On )
4	1 2 3	syl2anc	|- ( ph -> ( A +no B ) e. On )