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Theorem loolinALT 95
Description: The Linearity Axiom of the infinite-valued sentential logic (L-infinity) of Lukasiewicz. This version of loolin 173 does not use ax-3 7, meaning that this theorem is intuitionistically valid. (Contributed by O'Cat, 12-Aug-2004.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
loolinALT  |-  ( ( ( ph  ->  ps )  ->  ( ps  ->  ph ) )  ->  ( ps  ->  ph ) )

Proof of Theorem loolinALT
StepHypRef Expression
1 jarr 91 . 2  |-  ( ( ( ph  ->  ps )  ->  ( ps  ->  ph ) )  ->  ( ps  ->  ( ps  ->  ph ) ) )
21pm2.43d 44 1  |-  ( ( ( ph  ->  ps )  ->  ( ps  ->  ph ) )  ->  ( ps  ->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
  Copyright terms: Public domain W3C validator