Theorem necon3bi

Description: Contrapositive inference for inequality. (Contributed by NM, 1-Jun-2007) (Proof shortened by Andrew Salmon, 25-May-2011) (Proof shortened by Wolf Lammen, 22-Nov-2019)

	Ref	Expression
Hypothesis	necon3bi.1	|- ( A = B -> ph )
Assertion	necon3bi	|- ( -. ph -> A =/= B )

Proof

Step	Hyp	Ref	Expression
1		necon3bi.1	|- ( A = B -> ph )
2	1	con3i	|- ( -. ph -> -. A = B )
3	2	neqned	|- ( -. ph -> A =/= B )