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Theorem 3bitr2rd 206
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 180 . 2 (φ → (ψθ))
4 3bitr2d.3 . 2 (φ → (θτ))
53, 4bitr2d 178 1 (φ → (τψ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  fndmdif  5215  addsubeq4  7003  muleqadd  7411  nn0lt10b  8077  frec2uzltd  8850
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