Theorem divdiri

Description: Distribution of division over addition. (Contributed by NM, 16-Feb-1995)

	Ref	Expression
Hypotheses	divclz.1	|- A e. CC
	divclz.2	|- B e. CC
	divmulz.3	|- C e. CC
	divass.4	|- C =/= 0
Assertion	divdiri	|- ( ( A + B ) / C ) = ( ( A / C ) + ( B / C ) )

Proof

Step	Hyp	Ref	Expression
1		divclz.1	|- A e. CC
2		divclz.2	|- B e. CC
3		divmulz.3	|- C e. CC
4		divass.4	|- C =/= 0
5	1 2 3	divdirzi	|- ( C =/= 0 -> ( ( A + B ) / C ) = ( ( A / C ) + ( B / C ) ) )
6	4 5	ax-mp	|- ( ( A + B ) / C ) = ( ( A / C ) + ( B / C ) )