NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  re1tbw3 GIF version

Theorem re1tbw3 1512
Description: tbw-ax3 1467 rederived from merco2 1501. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
re1tbw3 (((φψ) → φ) → φ)

Proof of Theorem re1tbw3
StepHypRef Expression
1 mercolem2 1503 . 2 (((φφ) → φ) → (φ → (φφ)))
2 mercolem2 1503 . . 3 (((φψ) → φ) → ((((φφ) → φ) → (φ → (φφ))) → (((φψ) → φ) → φ)))
3 mercolem6 1507 . . 3 ((((φψ) → φ) → ((((φφ) → φ) → (φ → (φφ))) → (((φψ) → φ) → φ))) → ((((φφ) → φ) → (φ → (φφ))) → (((φψ) → φ) → φ)))
42, 3ax-mp 5 . 2 ((((φφ) → φ) → (φ → (φφ))) → (((φψ) → φ) → φ))
51, 4ax-mp 5 1 (((φψ) → φ) → φ)
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  ax-3 8
This theorem depends on definitions:  df-bi 177  df-tru 1319  df-fal 1320
This theorem is referenced by:  re1tbw4  1513
  Copyright terms: Public domain W3C validator