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Metamath Proof Explorer
Description: Alternate proof of pm2.21dd . (Contributed by Mario Carneiro, 9-Feb-2017) (Proof modification is discouraged.)
(New usage is discouraged.)
|
|
Ref |
Expression |
|
Hypotheses |
pm2.21ddALT.1 |
⊢ ( 𝜑 → 𝜓 ) |
|
|
pm2.21ddALT.2 |
⊢ ( 𝜑 → ¬ 𝜓 ) |
|
Assertion |
pm2.21ddALT |
⊢ ( 𝜑 → 𝜒 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
pm2.21ddALT.1 |
⊢ ( 𝜑 → 𝜓 ) |
| 2 |
|
pm2.21ddALT.2 |
⊢ ( 𝜑 → ¬ 𝜓 ) |
| 3 |
2
|
pm2.21d |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
| 4 |
1 3
|
mpd |
⊢ ( 𝜑 → 𝜒 ) |