Theorem nnaddcomli

Description: Version of addcomli for natural numbers. (Contributed by Steven Nguyen, 1-Aug-2023)

	Ref	Expression
Hypotheses	nnaddcomli.1	|- A e. NN
	nnaddcomli.2	|- B e. NN
	nnaddcomli.3	|- ( A + B ) = C
Assertion	nnaddcomli	|- ( B + A ) = C

Proof

Step	Hyp	Ref	Expression
1		nnaddcomli.1	|- A e. NN
2		nnaddcomli.2	|- B e. NN
3		nnaddcomli.3	|- ( A + B ) = C
4		nnaddcom	|- ( ( B e. NN /\ A e. NN ) -> ( B + A ) = ( A + B ) )
5	2 1 4	mp2an	|- ( B + A ) = ( A + B )
6	5 3	eqtri	|- ( B + A ) = C