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Theorem meran2 24851
Description: A single axiom for propositional calculus offered by Meredith. (Contributed by Anthony Hart, 13-Aug-2011.)
Assertion
Ref Expression
meran2  |-  ( -.  ( -.  ( -. 
ph  \/  ps )  \/  ( ch  \/  ( th  \/  ta ) ) )  \/  ( -.  ( -.  ta  \/  th )  \/  ( ch  \/  ( ph  \/  th ) ) ) )

Proof of Theorem meran2
StepHypRef Expression
1 meran1 24850 . . . 4  |-  ( -.  ( -.  ( -. 
ph  \/  ps )  \/  ( ch  \/  ( th  \/  ta ) ) )  \/  ( -.  ( -.  th  \/  ph )  \/  ( ch  \/  ( ta  \/  ph ) ) ) )
21imorri 403 . . 3  |-  ( ( -.  ( -.  ph  \/  ps )  \/  ( ch  \/  ( th  \/  ta ) ) )  -> 
( -.  ( -. 
th  \/  ph )  \/  ( ch  \/  ( ta  \/  ph ) ) ) )
3 meran1 24850 . . . 4  |-  ( -.  ( -.  ( -. 
th  \/  ph )  \/  ( ch  \/  ( ta  \/  ph ) ) )  \/  ( -.  ( -.  ta  \/  th )  \/  ( ch  \/  ( ph  \/  th ) ) ) )
43imorri 403 . . 3  |-  ( ( -.  ( -.  th  \/  ph )  \/  ( ch  \/  ( ta  \/  ph ) ) )  -> 
( -.  ( -. 
ta  \/  th )  \/  ( ch  \/  ( ph  \/  th ) ) ) )
52, 4syl 15 . 2  |-  ( ( -.  ( -.  ph  \/  ps )  \/  ( ch  \/  ( th  \/  ta ) ) )  -> 
( -.  ( -. 
ta  \/  th )  \/  ( ch  \/  ( ph  \/  th ) ) ) )
65imori 402 1  |-  ( -.  ( -.  ( -. 
ph  \/  ps )  \/  ( ch  \/  ( th  \/  ta ) ) )  \/  ( -.  ( -.  ta  \/  th )  \/  ( ch  \/  ( ph  \/  th ) ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    \/ wo 357
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-or 359
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