MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  tbwsyl Structured version   Visualization version   GIF version

Theorem tbwsyl 1669
Description: Used to rederive the Lukasiewicz axioms from Tarski-Bernays-Wajsberg'. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
tbwsyl.1 (𝜑𝜓)
tbwsyl.2 (𝜓𝜒)
Assertion
Ref Expression
tbwsyl (𝜑𝜒)

Proof of Theorem tbwsyl
StepHypRef Expression
1 tbwsyl.2 . 2 (𝜓𝜒)
2 tbwsyl.1 . . 3 (𝜑𝜓)
3 tbw-ax1 1665 . . 3 ((𝜑𝜓) → ((𝜓𝜒) → (𝜑𝜒)))
42, 3ax-mp 5 . 2 ((𝜓𝜒) → (𝜑𝜒))
51, 4ax-mp 5 1 (𝜑𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  tbwlem1  1670  tbwlem2  1671  tbwlem3  1672  tbwlem4  1673  tbwlem5  1674  re1luk2  1676
  Copyright terms: Public domain W3C validator