Theorem recidzi

Description: Multiplication of a number and its reciprocal. (Contributed by NM, 14-May-1999)

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

Proof

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