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Theorem wl-ax3 33255
Description: ax-3 8 proved from Lukasiewicz's axioms. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
wl-ax3 |- ( ( -. ph -> -. ps ) -> ( ps -> ph ) )
Proof of Theorem wl-ax3
StepHypRef Expression
1 ax-luk3 33243 . . 3 |- ( ps -> ( -. ps -> ph ) )
2 ax-luk1 33241 . . 3 |- ( ( -. ph -> -. ps ) -> ( ( -. ps -> ph ) -> ( -. ph -> ph ) ) )
31, 2wl-syl5 33247 . 2 |- ( ( -. ph -> -. ps ) -> ( ps -> ( -. ph -> ph ) ) )
4 ax-luk2 33242 . 2 |- ( ( -. ph -> ph ) -> ph )
53, 4wl-syl6 33254 1 |- ( ( -. ph -> -. ps ) -> ( ps -> ph ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3   -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-luk1 33241  ax-luk2 33242  ax-luk3 33243
This theorem is referenced by:  wl-ax1  33256
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