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Metamath Proof Explorer
Description: Deduction associated with pm2.86 . (Contributed by NM, 29-Jun-1995)
(Proof shortened by Wolf Lammen, 3-Apr-2013)
|
|
Ref |
Expression |
|
Hypothesis |
pm2.86d.1 |
⊢ ( 𝜑 → ( ( 𝜓 → 𝜒 ) → ( 𝜓 → 𝜃 ) ) ) |
|
Assertion |
pm2.86d |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
pm2.86d.1 |
⊢ ( 𝜑 → ( ( 𝜓 → 𝜒 ) → ( 𝜓 → 𝜃 ) ) ) |
| 2 |
|
ax-1 |
⊢ ( 𝜒 → ( 𝜓 → 𝜒 ) ) |
| 3 |
2 1
|
syl5 |
⊢ ( 𝜑 → ( 𝜒 → ( 𝜓 → 𝜃 ) ) ) |
| 4 |
3
|
com23 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) ) |