Theorem negdid

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

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

Proof

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