Theorem recne0zi

Description: The reciprocal of a nonzero number is nonzero. (Contributed by NM, 14-May-1999)

	Ref	Expression
Hypothesis	divclz.1	⊢ 𝐴 ∈ ℂ
Assertion	recne0zi	⊢ ( 𝐴 ≠ 0 → ( 1 / 𝐴 ) ≠ 0 )

Proof

Step	Hyp	Ref	Expression
1		divclz.1	⊢ 𝐴 ∈ ℂ
2		recne0	⊢ ( ( 𝐴 ∈ ℂ ∧ 𝐴 ≠ 0 ) → ( 1 / 𝐴 ) ≠ 0 )
3	1 2	mpan	⊢ ( 𝐴 ≠ 0 → ( 1 / 𝐴 ) ≠ 0 )