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Metamath Proof Explorer
Description: Importation deduction with commuted antecedents. (Contributed by Peter
Mazsa, 24-Sep-2022) (Proof shortened by Wolf Lammen, 22-Oct-2022)
|
|
Ref |
Expression |
|
Hypothesis |
impd.1 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) ) |
|
Assertion |
impcomd |
⊢ ( 𝜑 → ( ( 𝜒 ∧ 𝜓 ) → 𝜃 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
impd.1 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) ) |
| 2 |
1
|
com23 |
⊢ ( 𝜑 → ( 𝜒 → ( 𝜓 → 𝜃 ) ) ) |
| 3 |
2
|
impd |
⊢ ( 𝜑 → ( ( 𝜒 ∧ 𝜓 ) → 𝜃 ) ) |