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Theorem renicax 1530
Description: A rederivation of nic-ax 1506 from lukshef-ax1 1527, proving that lukshef-ax1 1527 with nic-mp 1504 can be used as a complete axiomatization of propositional calculus. (Contributed by Anthony Hart, 31-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
renicax

Proof of Theorem renicax
StepHypRef Expression
1 lukshefth1 1528 . . . 4
2 lukshefth2 1529 . . . 4
31, 2nic-mp 1504 . . 3
4 lukshefth2 1529 . . . 4
5 lukshef-ax1 1527 . . . 4
64, 5nic-mp 1504 . . 3
73, 6nic-mp 1504 . 2
8 lukshefth2 1529 . 2
97, 8nic-mp 1504 1
Colors of variables: wff setvar class
Syntax hints:  -/\wnan 1343
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 185  df-an 371  df-nan 1344
  Copyright terms: Public domain W3C validator