NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  3bitr2rd GIF version

Theorem 3bitr2rd 273
Description: Deduction from transitivity of biconditional. (Contributed by NM, 4-Aug-2006.)
Hypotheses
Ref Expression
3bitr2d.1 (φ → (ψχ))
3bitr2d.2 (φ → (θχ))
3bitr2d.3 (φ → (θτ))
Assertion
Ref Expression
3bitr2rd (φ → (τψ))

Proof of Theorem 3bitr2rd
StepHypRef Expression
1 3bitr2d.1 . . 3 (φ → (ψχ))
2 3bitr2d.2 . . 3 (φ → (θχ))
31, 2bitr4d 247 . 2 (φ → (ψθ))
4 3bitr2d.3 . 2 (φ → (θτ))
53, 4bitr2d 245 1 (φ → (τψ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176
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
This theorem is referenced by:  eqtfinrelk  4486
  Copyright terms: Public domain W3C validator