Theorem necon4ai

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	necon4ai.1	|- ( A =/= B -> -. ph )
Assertion	necon4ai	|- ( ph -> A = B )

Proof

Step	Hyp	Ref	Expression
1		necon4ai.1	|- ( A =/= B -> -. ph )
2		notnot	|- ( ph -> -. -. ph )
3	1	necon1bi	|- ( -. -. ph -> A = B )
4	2 3	syl	|- ( ph -> A = B )