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Metamath Proof Explorer
Description: Theorem *4.77 of WhiteheadRussell p. 121. (Contributed by NM, 3-Jan-2005)
|
|
Ref |
Expression |
|
Assertion |
pm4.77 |
⊢ ( ( ( 𝜓 → 𝜑 ) ∧ ( 𝜒 → 𝜑 ) ) ↔ ( ( 𝜓 ∨ 𝜒 ) → 𝜑 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
jaob |
⊢ ( ( ( 𝜓 ∨ 𝜒 ) → 𝜑 ) ↔ ( ( 𝜓 → 𝜑 ) ∧ ( 𝜒 → 𝜑 ) ) ) |
| 2 |
1
|
bicomi |
⊢ ( ( ( 𝜓 → 𝜑 ) ∧ ( 𝜒 → 𝜑 ) ) ↔ ( ( 𝜓 ∨ 𝜒 ) → 𝜑 ) ) |