Theorem resubidaddlid

Description: Any real number subtracted from itself forms a left additive identity. (Contributed by Steven Nguyen, 8-Jan-2023)

	Ref	Expression
Assertion	resubidaddlid	|- ( ( A e. RR /\ B e. RR ) -> ( ( A -R A ) + B ) = B )

Proof

Step	Hyp	Ref	Expression
1		readdsub	|- ( ( A e. RR /\ B e. RR /\ A e. RR ) -> ( ( A + B ) -R A ) = ( ( A -R A ) + B ) )
2	1	3anidm13	|- ( ( A e. RR /\ B e. RR ) -> ( ( A + B ) -R A ) = ( ( A -R A ) + B ) )
3		repncan2	|- ( ( A e. RR /\ B e. RR ) -> ( ( A + B ) -R A ) = B )
4	2 3	eqtr3d	|- ( ( A e. RR /\ B e. RR ) -> ( ( A -R A ) + B ) = B )