Description: Third property of three of the provability predicate. (Contributed by BJ, 3-Apr-2019)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | ax-prv3 | ⊢ ( Prv 𝜑 → Prv Prv 𝜑 ) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 0 | wph | ⊢ 𝜑 | |
| 1 | 0 | cprvb | ⊢ Prv 𝜑 | 
| 2 | 1 | cprvb | ⊢ Prv Prv 𝜑 | 
| 3 | 1 2 | wi | ⊢ ( Prv 𝜑 → Prv Prv 𝜑 ) |