MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  merlem2 Unicode version

Theorem merlem2 1398
Description: Step 4 of Meredith's proof of Lukasiewicz axioms from his sole axiom. (Contributed by NM, 14-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
merlem2  |-  ( ( ( ph  ->  ph )  ->  ch )  ->  ( th  ->  ch ) )

Proof of Theorem merlem2
StepHypRef Expression
1 merlem1 1397 . 2  |-  ( ( ( ( ch  ->  ch )  ->  ( -.  ph 
->  -.  th ) )  ->  ph )  ->  ( ph  ->  ph ) )
2 ax-meredith 1396 . 2  |-  ( ( ( ( ( ch 
->  ch )  ->  ( -.  ph  ->  -.  th )
)  ->  ph )  -> 
( ph  ->  ph )
)  ->  ( (
( ph  ->  ph )  ->  ch )  ->  ( th  ->  ch ) ) )
31, 2ax-mp 8 1  |-  ( ( ( ph  ->  ph )  ->  ch )  ->  ( th  ->  ch ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem is referenced by:  merlem3  1399  merlem12  1408
This theorem was proved from axioms:  ax-mp 8  ax-meredith 1396
  Copyright terms: Public domain W3C validator