Theorem naddcnffn

Description: Addition operator for Cantor normal forms is a function. (Contributed by RP, 2-Jan-2025)

	Ref	Expression
Assertion	naddcnffn	|- ( ( X e. On /\ S = dom ( _om CNF X ) ) -> ( oF +o |` ( S X. S ) ) Fn ( S X. S ) )

Proof

Step	Hyp	Ref	Expression
1		naddcnff	|- ( ( X e. On /\ S = dom ( _om CNF X ) ) -> ( oF +o |` ( S X. S ) ) : ( S X. S ) --> S )
2	1	ffnd	|- ( ( X e. On /\ S = dom ( _om CNF X ) ) -> ( oF +o |` ( S X. S ) ) Fn ( S X. S ) )