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| Mirrors > Home > MPE Home > Th. List > Mathboxes > ax-prv3 | Structured version Visualization version GIF version | ||
| Description: Third property of three of the provability predicate. (Contributed by BJ, 3-Apr-2019.) |
| Ref | Expression |
|---|---|
| ax-prv3 | ⊢ (Prv 𝜑 → Prv Prv 𝜑) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | wph | . . 3 wff 𝜑 | |
| 2 | 1 | cprvb 36598 | . 2 wff Prv 𝜑 |
| 3 | 2 | cprvb 36598 | . 2 wff Prv Prv 𝜑 |
| 4 | 2, 3 | wi 4 | 1 wff (Prv 𝜑 → Prv Prv 𝜑) |
| Colors of variables: wff setvar class |
| This axiom is referenced by: bj-babygodel 36604 bj-babylob 36605 |
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