Theorem divreczi

Description: Relationship between division and reciprocal. Theorem I.9 of Apostol p. 18. (Contributed by NM, 11-Oct-1999)

	Ref	Expression
Hypotheses	divclz.1	|- A e. CC
	divclz.2	|- B e. CC
Assertion	divreczi	|- ( B =/= 0 -> ( A / B ) = ( A x. ( 1 / B ) ) )

Proof

Step	Hyp	Ref	Expression
1		divclz.1	|- A e. CC
2		divclz.2	|- B e. CC
3		divrec	|- ( ( A e. CC /\ B e. CC /\ B =/= 0 ) -> ( A / B ) = ( A x. ( 1 / B ) ) )
4	1 2 3	mp3an12	|- ( B =/= 0 -> ( A / B ) = ( A x. ( 1 / B ) ) )