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Mirrors > Home > MPE Home > Th. List > nfri | Structured version Visualization version GIF version |
Description: Consequence of the definition of not-free. (Contributed by Wolf Lammen, 16-Sep-2021.) |
Ref | Expression |
---|---|
nfri.1 | ⊢ Ⅎ𝑥𝜑 |
Ref | Expression |
---|---|
nfri | ⊢ (∃𝑥𝜑 → ∀𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfri.1 | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | df-nf 1791 | . 2 ⊢ (Ⅎ𝑥𝜑 ↔ (∃𝑥𝜑 → ∀𝑥𝜑)) | |
3 | 1, 2 | mpbi 233 | 1 ⊢ (∃𝑥𝜑 → ∀𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1540 ∃wex 1786 Ⅎwnf 1790 |
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-nf 1791 |
This theorem is referenced by: nf5ri 2197 |
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