Theorem rerecid

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	rerecid	|- ( ph -> ( A x. ( 1 /R A ) ) = 1 )

Proof

Step	Hyp	Ref	Expression
1		sn-rereccld.a	|- ( ph -> A e. RR )
2		sn-rereccld.z	|- ( ph -> A =/= 0 )
3		1red	|- ( ph -> 1 e. RR )
4	3 1 2	redivcan2d	|- ( ph -> ( A x. ( 1 /R A ) ) = 1 )