Theorem recclzi

Description: Closure law for reciprocal. (Contributed by NM, 30-Apr-2005)

	Ref	Expression
Hypothesis	divclz.1	⊢ 𝐴 ∈ ℂ
Assertion	recclzi	⊢ ( 𝐴 ≠ 0 → ( 1 / 𝐴 ) ∈ ℂ )

Proof

Step	Hyp	Ref	Expression
1		divclz.1	⊢ 𝐴 ∈ ℂ
2		reccl	⊢ ( ( 𝐴 ∈ ℂ ∧ 𝐴 ≠ 0 ) → ( 1 / 𝐴 ) ∈ ℂ )
3	1 2	mpan	⊢ ( 𝐴 ≠ 0 → ( 1 / 𝐴 ) ∈ ℂ )