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Theorem 3bitrd 203
Description: Deduction from transitivity of biconditional. (Contributed by NM, 13-Aug-1999.)
Hypotheses
Ref Expression
3bitrd.1 (φ → (ψχ))
3bitrd.2 (φ → (χθ))
3bitrd.3 (φ → (θτ))
Assertion
Ref Expression
3bitrd (φ → (ψτ))

Proof of Theorem 3bitrd
StepHypRef Expression
1 3bitrd.1 . . 3 (φ → (ψχ))
2 3bitrd.2 . . 3 (φ → (χθ))
31, 2bitrd 177 . 2 (φ → (ψθ))
4 3bitrd.3 . 2 (φ → (θτ))
53, 4bitrd 177 1 (φ → (ψτ))
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:  sbceqal  2791  sbcnel12g  2844  elxp4  4735  elxp5  4736  f1eq123d  5046  foeq123d  5047  f1oeq123d  5048  ofrfval  5643  eloprabi  5745  smoeq  5827  ecidg  6081  enqbreq2  6216  ltanqg  6259
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