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Mirrors > Home > MPE Home > Th. List > lukshefax1  Unicode 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 nicmp 1431 for its constructions. Here, the axiom is proved as a substitution instance of nicax 1433. (Contributed by Anthony Hart, 31Jul2011.) (Proof modification is discouraged.) (New usage is discouraged.) 
Ref  Expression 

lukshefax1 
Step  Hyp  Ref  Expression 

1  nicax 1433  1 
Colors of variables: wff set class 
Syntax hints: wnan 1292 
This theorem is referenced by: lukshefth1 1455 lukshefth2 1456 renicax 1457 
This theorem was proved from axioms: ax1 7 ax2 8 ax3 9 axmp 10 
This theorem depends on definitions: dfbi 179 dfan 362 dfnan 1293 
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