Description: Closed form of sps . Once in main part, prove sps and spsd from it. (Contributed by BJ, 20-Oct-2019)
Ref | Expression | ||
---|---|---|---|
Assertion | bj-spst | ⊢ ( ( 𝜑 → 𝜓 ) → ( ∀ 𝑥 𝜑 → 𝜓 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sp | ⊢ ( ∀ 𝑥 𝜑 → 𝜑 ) | |
2 | 1 | imim1i | ⊢ ( ( 𝜑 → 𝜓 ) → ( ∀ 𝑥 𝜑 → 𝜓 ) ) |