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 ) ) |