Theorem negsubd

Description: Relationship between subtraction and negative. Theorem I.3 of Apostol p. 18. (Contributed by Mario Carneiro, 27-May-2016)

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

Proof

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