Theorem sn-redividd

Description: A number divided by itself is 1. (Contributed by SN, 2-Apr-2026)

	Ref	Expression
Hypotheses	sn-rediv0d.a	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
	sn-rediv0d.z	⊢ ( 𝜑 → 𝐴 ≠ 0 )
Assertion	sn-redividd	⊢ ( 𝜑 → ( 𝐴 /ℝ 𝐴 ) = 1 )

Proof

Step	Hyp	Ref	Expression
1		sn-rediv0d.a	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
2		sn-rediv0d.z	⊢ ( 𝜑 → 𝐴 ≠ 0 )
3		eqidd	⊢ ( 𝜑 → 𝐴 = 𝐴 )
4	1 1 2	rediveq1d	⊢ ( 𝜑 → ( ( 𝐴 /ℝ 𝐴 ) = 1 ↔ 𝐴 = 𝐴 ) )
5	3 4	mpbird	⊢ ( 𝜑 → ( 𝐴 /ℝ 𝐴 ) = 1 )