Description: Closed form of imim12i and of 3syl . (Contributed by BJ, 16-Jul-2019)
Ref | Expression | ||
---|---|---|---|
Assertion | imim12 | ⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜒 → 𝜃 ) → ( ( 𝜓 → 𝜒 ) → ( 𝜑 → 𝜃 ) ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imim2 | ⊢ ( ( 𝜒 → 𝜃 ) → ( ( 𝜓 → 𝜒 ) → ( 𝜓 → 𝜃 ) ) ) | |
2 | imim1 | ⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜓 → 𝜃 ) → ( 𝜑 → 𝜃 ) ) ) | |
3 | 1 2 | syl9r | ⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜒 → 𝜃 ) → ( ( 𝜓 → 𝜒 ) → ( 𝜑 → 𝜃 ) ) ) ) |