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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-nnfai | Structured version Visualization version GIF version |
Description: Nonfreeness implies the equivalent of ax-5 1917, inference form. See nf5ri 2197. (Contributed by BJ, 22-Sep-2024.) |
Ref | Expression |
---|---|
bj-nnfai.1 | ⊢ Ⅎ'𝑥𝜑 |
Ref | Expression |
---|---|
bj-nnfai | ⊢ (𝜑 → ∀𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-nnfai.1 | . 2 ⊢ Ⅎ'𝑥𝜑 | |
2 | bj-nnfa 34565 | . 2 ⊢ (Ⅎ'𝑥𝜑 → (𝜑 → ∀𝑥𝜑)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝜑 → ∀𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1540 Ⅎ'wnnf 34560 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 210 df-an 400 df-bj-nnf 34561 |
This theorem is referenced by: (None) |
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