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Mirrors > Home > MPE Home > Th. List > rbsyl | 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 |
---|---|
rbsyl.1 | ⊢ (¬ 𝜓 ∨ 𝜒) |
rbsyl.2 | ⊢ (𝜑 ∨ 𝜓) |
Ref | Expression |
---|---|
rbsyl | ⊢ (𝜑 ∨ 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rbsyl.2 | . 2 ⊢ (𝜑 ∨ 𝜓) | |
2 | rbsyl.1 | . . 3 ⊢ (¬ 𝜓 ∨ 𝜒) | |
3 | rb-ax1 1752 | . . 3 ⊢ (¬ (¬ 𝜓 ∨ 𝜒) ∨ (¬ (𝜑 ∨ 𝜓) ∨ (𝜑 ∨ 𝜒))) | |
4 | 2, 3 | anmp 1751 | . 2 ⊢ (¬ (𝜑 ∨ 𝜓) ∨ (𝜑 ∨ 𝜒)) |
5 | 1, 4 | anmp 1751 | 1 ⊢ (𝜑 ∨ 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∨ wo 845 |
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 206 df-an 398 df-or 846 |
This theorem is referenced by: rblem1 1757 rblem2 1758 rblem3 1759 rblem4 1760 rblem5 1761 rblem6 1762 re2luk1 1765 re2luk2 1766 re2luk3 1767 |
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