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Metamath Proof Explorer
Description: Importation inference (undistribute conjunction). (Contributed by NM, 20-Aug-1995)
|
|
Ref |
Expression |
|
Hypothesis |
3impdir.1 |
⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜓 ) ) → 𝜃 ) |
|
Assertion |
3impdir |
⊢ ( ( 𝜑 ∧ 𝜒 ∧ 𝜓 ) → 𝜃 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
3impdir.1 |
⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜓 ) ) → 𝜃 ) |
| 2 |
1
|
anandirs |
⊢ ( ( ( 𝜑 ∧ 𝜒 ) ∧ 𝜓 ) → 𝜃 ) |
| 3 |
2
|
3impa |
⊢ ( ( 𝜑 ∧ 𝜒 ∧ 𝜓 ) → 𝜃 ) |