Theorem negcon1ad

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

	Ref	Expression
Hypotheses	negidd.1	|- ( ph -> A e. CC )
	negcon1ad.2	|- ( ph -> -u A = B )
Assertion	negcon1ad	|- ( ph -> -u B = A )

Proof

Step	Hyp	Ref	Expression
1		negidd.1	|- ( ph -> A e. CC )
2		negcon1ad.2	|- ( ph -> -u A = B )
3	1	negcld	|- ( ph -> -u A e. CC )
4	2 3	eqeltrrd	|- ( ph -> B e. CC )
5	1 4	negcon1d	|- ( ph -> ( -u A = B <-> -u B = A ) )
6	2 5	mpbid	|- ( ph -> -u B = A )