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Theorem lukshef-ax1 1459
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)))))

Proof of Theorem lukshef-ax1
StepHypRef 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-mp 5  ax-1 6  ax-2 7  ax-3 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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