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Theorem luklem8 1420
Description: Used to rederive standard propositional axioms from Lukasiewicz'. (Contributed by NM, 22-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
luklem8  |-  ( (
ph  ->  ps )  -> 
( ( ch  ->  ph )  ->  ( ch  ->  ps ) ) )

Proof of Theorem luklem8
StepHypRef Expression
1 luk-1 1410 . 2  |-  ( ( ch  ->  ph )  -> 
( ( ph  ->  ps )  ->  ( ch  ->  ps ) ) )
2 luklem7 1419 . 2  |-  ( ( ( ch  ->  ph )  ->  ( ( ph  ->  ps )  ->  ( ch  ->  ps ) ) )  ->  ( ( ph  ->  ps )  ->  (
( ch  ->  ph )  ->  ( ch  ->  ps ) ) ) )
31, 2ax-mp 8 1  |-  ( (
ph  ->  ps )  -> 
( ( ch  ->  ph )  ->  ( ch  ->  ps ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  ax2  1422
This theorem was proved from axioms:  ax-mp 8  ax-meredith 1396
  Copyright terms: Public domain W3C validator