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| Mirrors > Home > MPE Home > Th. List > nfcri | Structured version Visualization version GIF version | ||
| Description: Consequence of the not-free predicate. (Contributed by Mario Carneiro, 11-Aug-2016.) Avoid ax-10 2141, ax-11 2157. (Revised by GG, 23-May-2024.) Avoid ax-12 2177 (adopting Wolf Lammen's 13-May-2023 proof). (Revised by SN, 3-Jun-2024.) |
| Ref | Expression |
|---|---|
| nfcri.1 | ⊢ Ⅎ𝑥𝐴 |
| Ref | Expression |
|---|---|
| nfcri | ⊢ Ⅎ𝑥 𝑦 ∈ 𝐴 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfcri.1 | . 2 ⊢ Ⅎ𝑥𝐴 | |
| 2 | nfcr 2895 | . 2 ⊢ (Ⅎ𝑥𝐴 → Ⅎ𝑥 𝑦 ∈ 𝐴) | |
| 3 | 1, 2 | ax-mp 5 | 1 ⊢ Ⅎ𝑥 𝑦 ∈ 𝐴 |
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