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Theorem loolin 173
Description: The Linearity Axiom of the infinite-valued sentential logic (L-infinity) of Lukasiewicz. For a version not using ax-3 7, see loolinALT 95. (Contributed by O'Cat, 12-Aug-2004.) (Proof shortened by Wolf Lammen, 2-Nov-2012.)
Assertion
Ref Expression
loolin  |-  ( ( ( ph  ->  ps )  ->  ( ps  ->  ph ) )  ->  ( ps  ->  ph ) )

Proof of Theorem loolin
StepHypRef Expression
1 pm2.521 146 . 2  |-  ( -.  ( ph  ->  ps )  ->  ( ps  ->  ph ) )
2 id 19 . 2  |-  ( ( ps  ->  ph )  -> 
( ps  ->  ph )
)
31, 2ja 153 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-3 7  ax-mp 8
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