Theorem negcon1d

Description: Contraposition law for unary minus. Deduction form of negcon1 . (Contributed by David Moews, 28-Feb-2017)

	Ref	Expression
Hypotheses	negidd.1	|- ( ph -> A e. CC )
	negcon1d.2	|- ( ph -> B e. CC )
Assertion	negcon1d	|- ( ph -> ( -u A = B <-> -u B = A ) )

Proof

Step	Hyp	Ref	Expression
1		negidd.1	|- ( ph -> A e. CC )
2		negcon1d.2	|- ( ph -> B e. CC )
3		negcon1	|- ( ( A e. CC /\ B e. CC ) -> ( -u A = B <-> -u B = A ) )
4	1 2 3	syl2anc	|- ( ph -> ( -u A = B <-> -u B = A ) )