Theorem sn-redivcld

Description: Closure law for real division. (Contributed by SN, 25-Nov-2025)

	Ref	Expression
Hypotheses	redivvald.a	$$⊢\phi \to A\in ℝ$$
	redivvald.b	$$⊢\phi \to B\in ℝ$$
	redivvald.z	$$⊢\phi \to B\ne 0$$
Assertion	sn-redivcld	Could not format assertion : No typesetting found for |- ( ph -> ( A /R B ) e. RR ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		redivvald.a	$$⊢\phi \to A\in ℝ$$
2		redivvald.b	$$⊢\phi \to B\in ℝ$$
3		redivvald.z	$$⊢\phi \to B\ne 0$$
4	1 2 3	redivvald	Could not format ( ph -> ( A /R B ) = ( iota_ x e. RR ( B x. x ) = A ) ) : No typesetting found for |- ( ph -> ( A /R B ) = ( iota_ x e. RR ( B x. x ) = A ) ) with typecode |-
5	1 2 3	rediveud	$$⊢\phi \to \exists !x\in ℝBx=A$$
6		riotacl	$$⊢\exists !x\in ℝBx=A\to \left(\iota x\in ℝ|Bx=A\right)\in ℝ$$
7	5 6	syl	$$⊢\phi \to \left(\iota x\in ℝ|Bx=A\right)\in ℝ$$
8	4 7	eqeltrd	Could not format ( ph -> ( A /R B ) e. RR ) : No typesetting found for |- ( ph -> ( A /R B ) e. RR ) with typecode |-