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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	⊢ ( ¬ ∀ 𝑥 𝑥 = 𝑦 → Ⅎ 𝑦 𝑥 )

Proof

Step	Hyp	Ref	Expression
1		nfcvf	⊢ ( ¬ ∀ 𝑦 𝑦 = 𝑥 → Ⅎ 𝑦 𝑥 )
2	1	naecoms	⊢ ( ¬ ∀ 𝑥 𝑥 = 𝑦 → Ⅎ 𝑦 𝑥 )