Description: A contraposition deduction. (Contributed by NM, 27-Dec-1992)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | con1d.1 | ⊢ ( 𝜑 → ( ¬ 𝜓 → 𝜒 ) ) | |
| Assertion | con1d | ⊢ ( 𝜑 → ( ¬ 𝜒 → 𝜓 ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | con1d.1 | ⊢ ( 𝜑 → ( ¬ 𝜓 → 𝜒 ) ) | |
| 2 | notnot | ⊢ ( 𝜒 → ¬ ¬ 𝜒 ) | |
| 3 | 1 2 | syl6 | ⊢ ( 𝜑 → ( ¬ 𝜓 → ¬ ¬ 𝜒 ) ) |
| 4 | 3 | con4d | ⊢ ( 𝜑 → ( ¬ 𝜒 → 𝜓 ) ) |