Theorem subeq0ad

Description: The difference of two complex numbers is zero iff they are equal. Deduction form of subeq0 . Generalization of subeq0d . (Contributed by David Moews, 28-Feb-2017)

	Ref	Expression
Hypotheses	negidd.1	|- ( ph -> A e. CC )
	pncand.2	|- ( ph -> B e. CC )
Assertion	subeq0ad	|- ( ph -> ( ( A - B ) = 0 <-> A = B ) )

Proof

Step	Hyp	Ref	Expression
1		negidd.1	|- ( ph -> A e. CC )
2		pncand.2	|- ( ph -> B e. CC )
3		subeq0	|- ( ( A e. CC /\ B e. CC ) -> ( ( A - B ) = 0 <-> A = B ) )
4	1 2 3	syl2anc	|- ( ph -> ( ( A - B ) = 0 <-> A = B ) )