Theorem int-mulsimpd

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

	Ref	Expression
Hypotheses	int-mulsimpd.1	|- ( ph -> B e. RR )
	int-mulsimpd.2	|- ( ph -> A = B )
	int-mulsimpd.3	|- ( ph -> B =/= 0 )
Assertion	int-mulsimpd	|- ( ph -> 1 = ( A / B ) )

Proof

Step	Hyp	Ref	Expression
1		int-mulsimpd.1	|- ( ph -> B e. RR )
2		int-mulsimpd.2	|- ( ph -> A = B )
3		int-mulsimpd.3	|- ( ph -> B =/= 0 )
4	1	recnd	|- ( ph -> B e. CC )
5	4 3 2	diveq1bd	|- ( ph -> ( A / B ) = 1 )
6	5	eqcomd	|- ( ph -> 1 = ( A / B ) )