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Mirrors > Home > LLPE Home > Th. List > mdasrd | Structured version |
Description: ⅋ is associative. Deduction form of mdasr 15. |
Ref | Expression |
---|---|
mdasrd.1 | ⊦ (𝜃 ⅋ (𝜑 ⅋ (𝜓 ⅋ 𝜒))) |
Ref | Expression |
---|---|
mdasrd | ⊦ (𝜃 ⅋ ((𝜑 ⅋ 𝜓) ⅋ 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mdasrd.1 | . 2 ⊦ (𝜃 ⅋ (𝜑 ⅋ (𝜓 ⅋ 𝜒))) | |
2 | mdasr 15 | . 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-mdco 8 ax-mdas 9 |
This theorem is referenced by: mdasri 17 |
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