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Metamath Proof Explorer

Theorem dveeq2

Description: Quantifier introduction when one pair of variables is distinct. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by NM, 2-Jan-2002) (Revised by NM, 20-Jul-2015) Remove dependency on ax-11 . (Revised by Wolf Lammen, 8-Sep-2018) (New usage is discouraged.)

		Ref	Expression
	Assertion	dveeq2	\|- ( -. A. x x = y -> ( z = y -> A. x z = y ) )

Proof

Step	Hyp	Ref	Expression
1		nfeqf2	\|- ( -. A. x x = y -> F/ x z = y )
2	1	nf5rd	\|- ( -. A. x x = y -> ( z = y -> A. x z = y ) )