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Metamath Proof Explorer

Theorem nfcvf2

Description: If x and y are distinct, then y is not free in x . Usage of this theorem is discouraged because it depends on ax-13 . See nfcv for a version that replaces the distinctor with a disjoint variable condition, requiring fewer axioms. (Contributed by Mario Carneiro, 5-Dec-2016) (New usage is discouraged.)

		Ref	Expression
	Assertion	nfcvf2	$⊢ \neg \forall x x = y \to \underline{Ⅎ} y x$

Proof

Step	Hyp	Ref	Expression
1		nfcvf	$⊢ \neg \forall y y = x \to \underline{Ⅎ} y x$
2	1	naecoms	$⊢ \neg \forall x x = y \to \underline{Ⅎ} y x$