Theorem int-add02d

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

	Ref	Expression
Hypotheses	int-add02d.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
	int-add02d.2	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	int-add02d	⊢ ( 𝜑 → ( 0 + 𝐴 ) = 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		int-add02d.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
2		int-add02d.2	⊢ ( 𝜑 → 𝐴 = 𝐵 )
3	1	recnd	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
4	3	addid2d	⊢ ( 𝜑 → ( 0 + 𝐴 ) = 𝐴 )
5	4 2	eqtrd	⊢ ( 𝜑 → ( 0 + 𝐴 ) = 𝐵 )