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Theorem lukshef-ax1 1468
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 1445 for its constructions.

Here, the axiom is proved as a substitution instance of nic-ax 1447. (Contributed by Anthony Hart, 31-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion
Ref Expression
lukshef-ax1  |-  ( (
ph  -/\  ( ch  -/\  ps ) )  -/\  (
( th  -/\  ( th  -/\  th ) ) 
-/\  ( ( th 
-/\  ch )  -/\  (
( ph  -/\  th )  -/\  ( ph  -/\  th )
) ) ) )

Proof of Theorem lukshef-ax1
StepHypRef Expression
1 nic-ax 1447 1  |-  ( (
ph  -/\  ( ch  -/\  ps ) )  -/\  (
( th  -/\  ( th  -/\  th ) ) 
-/\  ( ( th 
-/\  ch )  -/\  (
( ph  -/\  th )  -/\  ( ph  -/\  th )
) ) ) )
Colors of variables: wff set class
Syntax hints:    -/\ wnan 1296
This theorem is referenced by:  lukshefth1  1469  lukshefth2  1470  renicax  1471
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 178  df-an 361  df-nan 1297
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