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Theorem 3bitr4d 276
 Description: Deduction from transitivity of biconditional. Useful for converting conditional definitions in a formula. (Contributed by NM, 18-Oct-1995.)
Hypotheses
Ref Expression
3bitr4d.1 (φ → (ψχ))
3bitr4d.2 (φ → (θψ))
3bitr4d.3 (φ → (τχ))
Assertion
Ref Expression
3bitr4d (φ → (θτ))

Proof of Theorem 3bitr4d
StepHypRef Expression
1 3bitr4d.2 . 2 (φ → (θψ))
2 3bitr4d.1 . . 3 (φ → (ψχ))
3 3bitr4d.3 . . 3 (φ → (τχ))
42, 3bitr4d 247 . 2 (φ → (ψτ))
51, 4bitrd 244 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:  sbcom  2089  sbcom2  2114  r19.12sn  3789  lefinlteq  4463  eqtfinrelk  4486  tfinlefin  4502  opbrop  4841  fvopab3g  5386  unpreima  5408  inpreima  5409  respreima  5410  fconst5  5455  isotr  5495  ncseqnc  6128
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