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Theorem 3bitrrd 271
Description: Deduction from transitivity of biconditional. (Contributed by NM, 4-Aug-2006.)
Hypotheses
Ref Expression
3bitrd.1 (φ → (ψχ))
3bitrd.2 (φ → (χθ))
3bitrd.3 (φ → (θτ))
Assertion
Ref Expression
3bitrrd (φ → (τψ))

Proof of Theorem 3bitrrd
StepHypRef Expression
1 3bitrd.3 . 2 (φ → (θτ))
2 3bitrd.1 . . 3 (φ → (ψχ))
3 3bitrd.2 . . 3 (φ → (χθ))
42, 3bitr2d 245 . 2 (φ → (θψ))
51, 4bitr3d 246 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: (None)
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