Theorem sn-rediv0d

Description: Division into zero is zero. (Contributed by SN, 2-Apr-2026)

	Ref	Expression
Hypotheses	sn-rediv0d.a	|- ( ph -> A e. RR )
	sn-rediv0d.z	|- ( ph -> A =/= 0 )
Assertion	sn-rediv0d	|- ( ph -> ( 0 /R A ) = 0 )

Proof

Step	Hyp	Ref	Expression
1		sn-rediv0d.a	|- ( ph -> A e. RR )
2		sn-rediv0d.z	|- ( ph -> A =/= 0 )
3		eqidd	|- ( ph -> 0 = 0 )
4		0red	|- ( ph -> 0 e. RR )
5	4 1 2	rediveq0d	|- ( ph -> ( ( 0 /R A ) = 0 <-> 0 = 0 ) )
6	3 5	mpbird	|- ( ph -> ( 0 /R A ) = 0 )