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Theorem luklem5 1417
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
luklem5  |-  ( ph  ->  ( ps  ->  ph )
)

Proof of Theorem luklem5
StepHypRef Expression
1 luklem3 1415 . 2  |-  ( ph  ->  ( ( ( -. 
ph  ->  ph )  ->  ph )  ->  ( ps  ->  ph )
) )
2 luklem4 1416 . 2  |-  ( ( ( ( -.  ph  ->  ph )  ->  ph )  ->  ( ps  ->  ph )
)  ->  ( ps  ->  ph ) )
31, 2luklem1 1413 1  |-  ( ph  ->  ( ps  ->  ph )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem is referenced by:  luklem6  1418  luklem7  1419  ax1  1421
This theorem was proved from axioms:  ax-mp 8  ax-meredith 1396
  Copyright terms: Public domain W3C validator