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Metamath Proof Explorer
Description: Theorem *3.44 of WhiteheadRussell p. 113. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 3-Oct-2013)
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|
Ref |
Expression |
|
Assertion |
pm3.44 |
⊢ ( ( ( 𝜓 → 𝜑 ) ∧ ( 𝜒 → 𝜑 ) ) → ( ( 𝜓 ∨ 𝜒 ) → 𝜑 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
id |
⊢ ( ( 𝜓 → 𝜑 ) → ( 𝜓 → 𝜑 ) ) |
| 2 |
|
id |
⊢ ( ( 𝜒 → 𝜑 ) → ( 𝜒 → 𝜑 ) ) |
| 3 |
1 2
|
jaao |
⊢ ( ( ( 𝜓 → 𝜑 ) ∧ ( 𝜒 → 𝜑 ) ) → ( ( 𝜓 ∨ 𝜒 ) → 𝜑 ) ) |