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Metamath Proof Explorer
Description: A contradiction implies anything. Deduction associated with pm2.21 .
(Contributed by NM, 10-Feb-1996)
|
|
Ref |
Expression |
|
Hypothesis |
pm2.21d.1 |
⊢ ( 𝜑 → ¬ 𝜓 ) |
|
Assertion |
pm2.21d |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
pm2.21d.1 |
⊢ ( 𝜑 → ¬ 𝜓 ) |
| 2 |
1
|
a1d |
⊢ ( 𝜑 → ( ¬ 𝜒 → ¬ 𝜓 ) ) |
| 3 |
2
|
con4d |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |