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Metamath Proof Explorer

Theorem nfcvd

Description: If x is disjoint from A , then x is not free in A . (Contributed by Mario Carneiro, 7-Oct-2016)

Ref Expression
Assertion nfcvd ⊢ φ → Ⅎ _ x A

Proof

Step Hyp Ref Expression
1 nfcv ⊢ Ⅎ _ x A
2 1 a1i ⊢ φ → Ⅎ _ x A