Metamath Proof Explorer


Theorem luk-3

Description: 3 of 3 axioms for propositional calculus due to Lukasiewicz, derived from Meredith's sole axiom. (Contributed by NM, 14-Dec-2002) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion luk-3
|- ( ph -> ( -. ph -> ps ) )

Proof

Step Hyp Ref Expression
1 merlem11
 |-  ( ( -. ph -> ( -. ph -> ps ) ) -> ( -. ph -> ps ) )
2 merlem1
 |-  ( ( ( -. ph -> ( -. ph -> ps ) ) -> ( -. ph -> ps ) ) -> ( ph -> ( -. ph -> ps ) ) )
3 1 2 ax-mp
 |-  ( ph -> ( -. ph -> ps ) )