Theorem int-addsimpd

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

	Ref	Expression
Hypotheses	int-addsimpd.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
	int-addsimpd.2	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	int-addsimpd	⊢ ( 𝜑 → 0 = ( 𝐴 − 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		int-addsimpd.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
2		int-addsimpd.2	⊢ ( 𝜑 → 𝐴 = 𝐵 )
3	1	recnd	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
4	3 2	subeq0bd	⊢ ( 𝜑 → ( 𝐴 − 𝐵 ) = 0 )
5	4	eqcomd	⊢ ( 𝜑 → 0 = ( 𝐴 − 𝐵 ) )