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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-nnfei | Structured version Visualization version GIF version |
Description: Nonfreeness implies the equivalent of ax5e 1919, inference form. (Contributed by BJ, 22-Sep-2024.) |
Ref | Expression |
---|---|
bj-nnfei.1 | ⊢ Ⅎ'𝑥𝜑 |
Ref | Expression |
---|---|
bj-nnfei | ⊢ (∃𝑥𝜑 → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-nnfei.1 | . 2 ⊢ Ⅎ'𝑥𝜑 | |
2 | bj-nnfe 34568 | . 2 ⊢ (Ⅎ'𝑥𝜑 → (∃𝑥𝜑 → 𝜑)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (∃𝑥𝜑 → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wex 1786 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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