Theorem negsubdid

Description: Distribution of negative over subtraction. (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypotheses	negidd.1	|- ( ph -> A e. CC )
	pncand.2	|- ( ph -> B e. CC )
Assertion	negsubdid	|- ( ph -> -u ( A - B ) = ( -u A + B ) )

Proof

Step	Hyp	Ref	Expression
1		negidd.1	|- ( ph -> A e. CC )
2		pncand.2	|- ( ph -> B e. CC )
3		negsubdi	|- ( ( A e. CC /\ B e. CC ) -> -u ( A - B ) = ( -u A + B ) )
4	1 2 3	syl2anc	|- ( ph -> -u ( A - B ) = ( -u A + B ) )