Theorem int-mul12d

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

	Ref	Expression
Hypotheses	int-mul12d.1	$$⊢\phi \to A\in ℝ$$
	int-mul12d.2	$$⊢\phi \to A=B$$
Assertion	int-mul12d	$$⊢\phi \to 1A=B$$

Proof

Step	Hyp	Ref	Expression
1		int-mul12d.1	$$⊢\phi \to A\in ℝ$$
2		int-mul12d.2	$$⊢\phi \to A=B$$
3	1	recnd	$$⊢\phi \to A\in ℂ$$
4	3	mullidd	$$⊢\phi \to 1A=A$$
5	4 2	eqtrd	$$⊢\phi \to 1A=B$$