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Theorem 3bitr3d 207
Description: Deduction from transitivity of biconditional. Useful for converting conditional definitions in a formula. (Contributed by NM, 24-Apr-1996.)
Hypotheses
Ref Expression
3bitr3d.1 (φ → (ψχ))
3bitr3d.2 (φ → (ψθ))
3bitr3d.3 (φ → (χτ))
Assertion
Ref Expression
3bitr3d (φ → (θτ))

Proof of Theorem 3bitr3d
StepHypRef Expression
1 3bitr3d.2 . . 3 (φ → (ψθ))
2 3bitr3d.1 . . 3 (φ → (ψχ))
31, 2bitr3d 179 . 2 (φ → (θχ))
4 3bitr3d.3 . 2 (φ → (χτ))
53, 4bitrd 177 1 (φ → (θτ))
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:  csbcomg  2867  eloprabga  5533  ereldm  6085  subcan  7062  conjmulap  7487  ltrec  7630  divelunit  8640  fseq1m1p1  8727  fzm1  8732
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