Linear Logic Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > LLPE Home > Th. List > mdasd | Structured version |
Description: ⅋ is associative. Deduction form of ax-mdas 9. |
Ref | Expression |
---|---|
mdasd.1 | ⊦ (𝜃 ⅋ ((𝜑 ⅋ 𝜓) ⅋ 𝜒)) |
Ref | Expression |
---|---|
mdasd | ⊦ (𝜃 ⅋ (𝜑 ⅋ (𝜓 ⅋ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mdasd.1 | . 2 ⊦ (𝜃 ⅋ ((𝜑 ⅋ 𝜓) ⅋ 𝜒)) | |
2 | ax-mdas 9 | . 2 ⊦ (~ ((𝜑 ⅋ 𝜓) ⅋ 𝜒) ⅋ (𝜑 ⅋ (𝜓 ⅋ 𝜒))) | |
3 | 1, 2 | ax-cut 6 | 1 ⊦ (𝜃 ⅋ (𝜑 ⅋ (𝜓 ⅋ 𝜒))) |
Colors of variables: wff var nilad |
Syntax hints: ⅋ wmd 2 |
This theorem was proved from axioms: ax-cut 6 ax-mdas 9 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |