Theorem int-addcomd

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

	Ref	Expression
Hypotheses	int-addcomd.1	$$⊢\phi \to B\in ℝ$$
	int-addcomd.2	$$⊢\phi \to C\in ℝ$$
	int-addcomd.3	$$⊢\phi \to A=B$$
Assertion	int-addcomd	$$⊢\phi \to B+C=C+A$$

Proof

Step	Hyp	Ref	Expression
1		int-addcomd.1	$$⊢\phi \to B\in ℝ$$
2		int-addcomd.2	$$⊢\phi \to C\in ℝ$$
3		int-addcomd.3	$$⊢\phi \to A=B$$
4	1	recnd	$$⊢\phi \to B\in ℂ$$
5	2	recnd	$$⊢\phi \to C\in ℂ$$
6	4 5	addcomd	$$⊢\phi \to B+C=C+B$$
7	3	eqcomd	$$⊢\phi \to B=A$$
8	7	oveq2d	$$⊢\phi \to C+B=C+A$$
9	6 8	eqtrd	$$⊢\phi \to B+C=C+A$$