Theorem necon2ai

Description: Contrapositive inference for inequality. (Contributed by NM, 16-Jan-2007) (Proof shortened by Andrew Salmon, 25-May-2011) (Proof shortened by Wolf Lammen, 22-Nov-2019)

	Ref	Expression
Hypothesis	necon2ai.1	|- ( A = B -> -. ph )
Assertion	necon2ai	|- ( ph -> A =/= B )

Proof

Step	Hyp	Ref	Expression
1		necon2ai.1	|- ( A = B -> -. ph )
2	1	con2i	|- ( ph -> -. A = B )
3	2	neqned	|- ( ph -> A =/= B )