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Mirrors > Home > MPE Home > Th. List > rblem3 | Structured version Visualization version GIF version |
Description: Used to rederive the Lukasiewicz axioms from Russell-Bernays'. (Contributed by Anthony Hart, 18-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
rblem3 | ⊢ (¬ (𝜒 ∨ 𝜑) ∨ ((𝜒 ∨ 𝜓) ∨ 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rb-ax2 1760 | . 2 ⊢ (¬ (𝜑 ∨ (𝜒 ∨ 𝜓)) ∨ ((𝜒 ∨ 𝜓) ∨ 𝜑)) | |
2 | rblem2 1765 | . . 3 ⊢ (¬ (𝜑 ∨ 𝜒) ∨ (𝜑 ∨ (𝜒 ∨ 𝜓))) | |
3 | rb-ax2 1760 | . . 3 ⊢ (¬ (𝜒 ∨ 𝜑) ∨ (𝜑 ∨ 𝜒)) | |
4 | 2, 3 | rbsyl 1763 | . 2 ⊢ (¬ (𝜒 ∨ 𝜑) ∨ (𝜑 ∨ (𝜒 ∨ 𝜓))) |
5 | 1, 4 | rbsyl 1763 | 1 ⊢ (¬ (𝜒 ∨ 𝜑) ∨ ((𝜒 ∨ 𝜓) ∨ 𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∨ wo 846 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 847 |
This theorem is referenced by: rblem6 1769 |
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