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Mirrors > Home > NFE Home > Th. List > lukshef-ax1 | GIF version |
Description: This alternative axiom
for propositional calculus using the Sheffer Stroke
was offered by Lukasiewicz in his Selected Works. It improves on Nicod's
axiom by reducing its number of variables by one.
This axiom also uses nic-mp 1436 for its constructions. Here, the axiom is proved as a substitution instance of nic-ax 1438. (Contributed by Anthony Hart, 31-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
lukshef-ax1 | ⊢ ((φ ⊼ (χ ⊼ ψ)) ⊼ ((θ ⊼ (θ ⊼ θ)) ⊼ ((θ ⊼ χ) ⊼ ((φ ⊼ θ) ⊼ (φ ⊼ θ))))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nic-ax 1438 | 1 ⊢ ((φ ⊼ (χ ⊼ ψ)) ⊼ ((θ ⊼ (θ ⊼ θ)) ⊼ ((θ ⊼ χ) ⊼ ((φ ⊼ θ) ⊼ (φ ⊼ θ))))) |
Colors of variables: wff setvar class |
Syntax hints: ⊼ wnan 1287 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 |
This theorem depends on definitions: df-bi 177 df-an 360 df-nan 1288 |
This theorem is referenced by: lukshefth1 1460 lukshefth2 1461 renicax 1462 |
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