Description: A symmetry with -> .
See negsym1 for more information. (Contributed by Anthony Hart, 4-Sep-2011)
Ref | Expression | ||
---|---|---|---|
Assertion | imsym1 | ⊢ ( ( 𝜓 → ( 𝜓 → ⊥ ) ) → ( 𝜓 → 𝜑 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.21 | ⊢ ( ¬ 𝜓 → ( 𝜓 → 𝜑 ) ) | |
2 | falim | ⊢ ( ⊥ → 𝜑 ) | |
3 | 2 | imim2i | ⊢ ( ( 𝜓 → ⊥ ) → ( 𝜓 → 𝜑 ) ) |
4 | 1 3 | ja | ⊢ ( ( 𝜓 → ( 𝜓 → ⊥ ) ) → ( 𝜓 → 𝜑 ) ) |