Description: If a implies b, then a implies not not b. (Contributed by Jarvin Udandy, 28-Aug-2016)
Ref | Expression | ||
---|---|---|---|
Assertion | atbiffatnnb | ⊢ ( ( 𝜑 → 𝜓 ) → ( 𝜑 → ¬ ¬ 𝜓 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | idd | ⊢ ( 𝜑 → ( 𝜓 → 𝜓 ) ) | |
2 | notnotb | ⊢ ( 𝜓 ↔ ¬ ¬ 𝜓 ) | |
3 | 1 2 | syl6ib | ⊢ ( 𝜑 → ( 𝜓 → ¬ ¬ 𝜓 ) ) |
4 | 3 | a2i | ⊢ ( ( 𝜑 → 𝜓 ) → ( 𝜑 → ¬ ¬ 𝜓 ) ) |