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Theorem 3bitr3g 278
 Description: More general version of 3bitr3i 266. Useful for converting definitions in a formula. (Contributed by NM, 4-Jun-1995.)
Hypotheses
Ref Expression
3bitr3g.1 (φ → (ψχ))
3bitr3g.2 (ψθ)
3bitr3g.3 (χτ)
Assertion
Ref Expression
3bitr3g (φ → (θτ))

Proof of Theorem 3bitr3g
StepHypRef Expression
1 3bitr3g.2 . . 3 (ψθ)
2 3bitr3g.1 . . 3 (φ → (ψχ))
31, 2syl5bbr 250 . 2 (φ → (θχ))
4 3bitr3g.3 . 2 (χτ)
53, 4syl6bb 252 1 (φ → (θτ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 177 This theorem is referenced by:  notbid  285  cador  1391  equequ2  1686  dfsbcq2  3049  unineq  3505  iindif2  4035  isoini  5497  brcupg  5814  enprmaplem3  6078  nmembers1lem3  6270
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