NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  merco1lem15 GIF version

Theorem merco1lem15 1496
Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1478. (Contributed by Anthony Hart, 18-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
merco1lem15 ((φψ) → (φ → (χψ)))

Proof of Theorem merco1lem15
StepHypRef Expression
1 merco1lem14 1495 . 2 ((((φψ) → ψ) → (χψ)) → (φ → (χψ)))
2 merco1lem13 1494 . 2 (((((φψ) → ψ) → (χψ)) → (φ → (χψ))) → ((φψ) → (φ → (χψ))))
31, 2ax-mp 5 1 ((φψ) → (φ → (χψ)))
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:  merco1lem16  1497  retbwax1  1500
  Copyright terms: Public domain W3C validator