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Metamath Proof Explorer

Theorem nfcri

Description: Consequence of the not-free predicate. (Contributed by Mario Carneiro, 11-Aug-2016) Avoid ax-10 , ax-11 . (Revised by GG, 23-May-2024) Avoid ax-12 (adopting Wolf Lammen's 13-May-2023 proof). (Revised by SN, 3-Jun-2024)

Ref Expression
Hypothesis nfcri.1 ⊢ Ⅎ _ x A
Assertion nfcri ⊢ Ⅎ x y ∈ A

Proof

Step Hyp Ref Expression
1 nfcri.1 ⊢ Ⅎ _ x A
2 nfcr ⊢ Ⅎ _ x A → Ⅎ x y ∈ A
3 1 2 ax-mp ⊢ Ⅎ x y ∈ A