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Theorem tbwsyl 1459
Description: Used to rederive the Lukasiewicz axioms from Tarski-Bernays-Wajsberg'. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
tbwsyl.1  |-  ( ph  ->  ps )
tbwsyl.2  |-  ( ps 
->  ch )
Assertion
Ref Expression
tbwsyl  |-  ( ph  ->  ch )

Proof of Theorem tbwsyl
StepHypRef Expression
1 tbwsyl.2 . 2  |-  ( ps 
->  ch )
2 tbwsyl.1 . . 3  |-  ( ph  ->  ps )
3 tbw-ax1 1455 . . 3  |-  ( (
ph  ->  ps )  -> 
( ( ps  ->  ch )  ->  ( ph  ->  ch ) ) )
42, 3ax-mp 8 . 2  |-  ( ( ps  ->  ch )  ->  ( ph  ->  ch ) )
51, 4ax-mp 8 1  |-  ( ph  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  tbwlem1  1460  tbwlem2  1461  tbwlem3  1462  tbwlem4  1463  tbwlem5  1464  re1luk2  1466
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
  Copyright terms: Public domain W3C validator