Theorem rerecid2d

Description: Multiplication of a number and its reciprocal. (Contributed by SN, 25-Nov-2025)

	Ref	Expression
Hypotheses	sn-rereccld.a	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
	sn-rereccld.z	⊢ ( 𝜑 → 𝐴 ≠ 0 )
Assertion	rerecid2d	⊢ ( 𝜑 → ( ( 1 /ℝ 𝐴 ) · 𝐴 ) = 1 )

Proof

Step	Hyp	Ref	Expression
1		sn-rereccld.a	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
2		sn-rereccld.z	⊢ ( 𝜑 → 𝐴 ≠ 0 )
3	1 2	sn-rereccld	⊢ ( 𝜑 → ( 1 /ℝ 𝐴 ) ∈ ℝ )
4	1 2	rerecidd	⊢ ( 𝜑 → ( 𝐴 · ( 1 /ℝ 𝐴 ) ) = 1 )
5	1 3 4	remulinvcom	⊢ ( 𝜑 → ( ( 1 /ℝ 𝐴 ) · 𝐴 ) = 1 )