Theorem recdiv2

Description: Division into a reciprocal. (Contributed by NM, 19-Oct-2007)

	Ref	Expression
Assertion	recdiv2	⊢ ( ( ( 𝐴 ∈ ℂ ∧ 𝐴 ≠ 0 ) ∧ ( 𝐵 ∈ ℂ ∧ 𝐵 ≠ 0 ) ) → ( ( 1 / 𝐴 ) / 𝐵 ) = ( 1 / ( 𝐴 · 𝐵 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ax-1cn	⊢ 1 ∈ ℂ
2		divdiv1	⊢ ( ( 1 ∈ ℂ ∧ ( 𝐴 ∈ ℂ ∧ 𝐴 ≠ 0 ) ∧ ( 𝐵 ∈ ℂ ∧ 𝐵 ≠ 0 ) ) → ( ( 1 / 𝐴 ) / 𝐵 ) = ( 1 / ( 𝐴 · 𝐵 ) ) )
3	1 2	mp3an1	⊢ ( ( ( 𝐴 ∈ ℂ ∧ 𝐴 ≠ 0 ) ∧ ( 𝐵 ∈ ℂ ∧ 𝐵 ≠ 0 ) ) → ( ( 1 / 𝐴 ) / 𝐵 ) = ( 1 / ( 𝐴 · 𝐵 ) ) )