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 ) |