Theorem pm2.61ine

Description: Inference eliminating an inequality in an antecedent. (Contributed by NM, 16-Jan-2007) (Proof shortened by Andrew Salmon, 25-May-2011)

	Ref	Expression
Hypotheses	pm2.61ine.1	|- ( A = B -> ph )
	pm2.61ine.2	|- ( A =/= B -> ph )
Assertion	pm2.61ine	|- ph

Proof

Step	Hyp	Ref	Expression
1		pm2.61ine.1	|- ( A = B -> ph )
2		pm2.61ine.2	|- ( A =/= B -> ph )
3		nne	|- ( -. A =/= B <-> A = B )
4	3 1	sylbi	|- ( -. A =/= B -> ph )
5	2 4	pm2.61i	|- ph