Theorem rerecid2

Description: Multiplication of a number and its reciprocal. (Contributed by SN, 25-Nov-2025)

	Ref	Expression
Hypotheses	sn-rereccld.a	|- ( ph -> A e. RR )
	sn-rereccld.z	|- ( ph -> A =/= 0 )
Assertion	rerecid2	|- ( ph -> ( ( 1 /R A ) x. A ) = 1 )

Proof

Step	Hyp	Ref	Expression
1		sn-rereccld.a	|- ( ph -> A e. RR )
2		sn-rereccld.z	|- ( ph -> A =/= 0 )
3	1 2	sn-rereccld	|- ( ph -> ( 1 /R A ) e. RR )
4	1 2	rerecid	|- ( ph -> ( A x. ( 1 /R A ) ) = 1 )
5	1 3 4	remulinvcom	|- ( ph -> ( ( 1 /R A ) x. A ) = 1 )