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Metamath Proof Explorer
Description: Theorem *2.8 of WhiteheadRussell p. 108. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 5-Jan-2013)
|
|
Ref |
Expression |
|
Assertion |
pm2.8 |
⊢ ( ( 𝜑 ∨ 𝜓 ) → ( ( ¬ 𝜓 ∨ 𝜒 ) → ( 𝜑 ∨ 𝜒 ) ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
pm2.53 |
⊢ ( ( 𝜑 ∨ 𝜓 ) → ( ¬ 𝜑 → 𝜓 ) ) |
| 2 |
1
|
con1d |
⊢ ( ( 𝜑 ∨ 𝜓 ) → ( ¬ 𝜓 → 𝜑 ) ) |
| 3 |
2
|
orim1d |
⊢ ( ( 𝜑 ∨ 𝜓 ) → ( ( ¬ 𝜓 ∨ 𝜒 ) → ( 𝜑 ∨ 𝜒 ) ) ) |