Theorem negne0d

Description: The negative of a nonzero number is nonzero. (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypotheses	negidd.1	|- ( ph -> A e. CC )
	negne0d.2	|- ( ph -> A =/= 0 )
Assertion	negne0d	|- ( ph -> -u A =/= 0 )

Proof

Step	Hyp	Ref	Expression
1		negidd.1	|- ( ph -> A e. CC )
2		negne0d.2	|- ( ph -> A =/= 0 )
3	1	negne0bd	|- ( ph -> ( A =/= 0 <-> -u A =/= 0 ) )
4	2 3	mpbid	|- ( ph -> -u A =/= 0 )