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Metamath Proof Explorer
Description: Theorem *3.43 (Comp) of WhiteheadRussell p. 113. (Contributed by NM, 3-Jan-2005)
|
|
Ref |
Expression |
|
Assertion |
pm3.43 |
⊢ ( ( ( 𝜑 → 𝜓 ) ∧ ( 𝜑 → 𝜒 ) ) → ( 𝜑 → ( 𝜓 ∧ 𝜒 ) ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
pm3.43i |
⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜑 → 𝜒 ) → ( 𝜑 → ( 𝜓 ∧ 𝜒 ) ) ) ) |
| 2 |
1
|
imp |
⊢ ( ( ( 𝜑 → 𝜓 ) ∧ ( 𝜑 → 𝜒 ) ) → ( 𝜑 → ( 𝜓 ∧ 𝜒 ) ) ) |