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Metamath Proof Explorer

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