Theorem int-addsimpd

Description: AdditionSimplification generator rule. (Contributed by Stanislas Polu, 7-Apr-2020)

	Ref	Expression
Hypotheses	int-addsimpd.1	$$⊢\phi \to A\in ℝ$$
	int-addsimpd.2	$$⊢\phi \to A=B$$
Assertion	int-addsimpd	$$⊢\phi \to 0=A-B$$

Proof

Step	Hyp	Ref	Expression
1		int-addsimpd.1	$$⊢\phi \to A\in ℝ$$
2		int-addsimpd.2	$$⊢\phi \to A=B$$
3	1	recnd	$$⊢\phi \to A\in ℂ$$
4	3 2	subeq0bd	$$⊢\phi \to A-B=0$$
5	4	eqcomd	$$⊢\phi \to 0=A-B$$