Theorem neg11d

Description: If the difference between two numbers is zero, they are equal. (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypotheses	negidd.1	|- ( ph -> A e. CC )
	pncand.2	|- ( ph -> B e. CC )
	neg11d.3	|- ( ph -> -u A = -u B )
Assertion	neg11d	|- ( ph -> A = B )

Proof

Step	Hyp	Ref	Expression
1		negidd.1	|- ( ph -> A e. CC )
2		pncand.2	|- ( ph -> B e. CC )
3		neg11d.3	|- ( ph -> -u A = -u B )
4	1 2	neg11ad	|- ( ph -> ( -u A = -u B <-> A = B ) )
5	3 4	mpbid	|- ( ph -> A = B )