MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax3 Unicode version

Theorem ax3 1423
Description: Standard propositional axiom derived from Lukasiewicz axioms. (Contributed by NM, 22-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax3  |-  ( ( -.  ph  ->  -.  ps )  ->  ( ps  ->  ph ) )

Proof of Theorem ax3
StepHypRef Expression
1 luklem2 1414 . 2  |-  ( ( -.  ph  ->  -.  ps )  ->  ( ( ( -.  ph  ->  ph )  ->  ph )  ->  ( ps  ->  ph ) ) )
2 luklem4 1416 . 2  |-  ( ( ( ( -.  ph  ->  ph )  ->  ph )  ->  ( ps  ->  ph )
)  ->  ( ps  ->  ph ) )
31, 2luklem1 1413 1  |-  ( ( -.  ph  ->  -.  ps )  ->  ( ps  ->  ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-mp 8  ax-meredith 1396
  Copyright terms: Public domain W3C validator