Theorem divreci

Description: Relationship between division and reciprocal. Theorem I.9 of Apostol p. 18. (Contributed by NM, 9-Feb-1995)

	Ref	Expression
Hypotheses	divclz.1	|- A e. CC
	divclz.2	|- B e. CC
	divcl.3	|- B =/= 0
Assertion	divreci	|- ( A / B ) = ( A x. ( 1 / B ) )

Proof

Step	Hyp	Ref	Expression
1		divclz.1	|- A e. CC
2		divclz.2	|- B e. CC
3		divcl.3	|- B =/= 0
4	1 2	divreczi	|- ( B =/= 0 -> ( A / B ) = ( A x. ( 1 / B ) ) )
5	3 4	ax-mp	|- ( A / B ) = ( A x. ( 1 / B ) )