Theorem sn-rereccld

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

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

Proof

Step	Hyp	Ref	Expression
1		sn-rereccld.a	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
2		sn-rereccld.z	⊢ ( 𝜑 → 𝐴 ≠ 0 )
3		1red	⊢ ( 𝜑 → 1 ∈ ℝ )
4	3 1 2	sn-redivcld	⊢ ( 𝜑 → ( 1 /ℝ 𝐴 ) ∈ ℝ )