Theorem int-mul12d

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

	Ref	Expression
Hypotheses	int-mul12d.1	|- ( ph -> A e. RR )
	int-mul12d.2	|- ( ph -> A = B )
Assertion	int-mul12d	|- ( ph -> ( 1 x. A ) = B )

Proof

Step	Hyp	Ref	Expression
1		int-mul12d.1	|- ( ph -> A e. RR )
2		int-mul12d.2	|- ( ph -> A = B )
3	1	recnd	|- ( ph -> A e. CC )
4	3	mullidd	|- ( ph -> ( 1 x. A ) = A )
5	4 2	eqtrd	|- ( ph -> ( 1 x. A ) = B )