Theorem nemtbir

Description: An inference from an inequality, related to modus tollens. (Contributed by NM, 13-Apr-2007)

	Ref	Expression
Hypotheses	nemtbir.1	|- A =/= B
	nemtbir.2	|- ( ph <-> A = B )
Assertion	nemtbir	|- -. ph

Proof

Step	Hyp	Ref	Expression
1		nemtbir.1	|- A =/= B
2		nemtbir.2	|- ( ph <-> A = B )
3	1	neii	|- -. A = B
4	3 2	mtbir	|- -. ph