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Metamath Proof Explorer
Description: Nested conjunction of antecedents. (Contributed by NM, 4-Jan-1993)
|
|
Ref |
Expression |
|
Assertion |
pm3.43i |
⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜑 → 𝜒 ) → ( 𝜑 → ( 𝜓 ∧ 𝜒 ) ) ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
pm3.2 |
⊢ ( 𝜓 → ( 𝜒 → ( 𝜓 ∧ 𝜒 ) ) ) |
| 2 |
1
|
imim3i |
⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜑 → 𝜒 ) → ( 𝜑 → ( 𝜓 ∧ 𝜒 ) ) ) ) |