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Theorem 3imtr3d 191
Description: More general version of 3imtr3i 189. Useful for converting conditional definitions in a formula. (Contributed by NM, 8-Apr-1996.)
Hypotheses
Ref Expression
3imtr3d.1 (φ → (ψχ))
3imtr3d.2 (φ → (ψθ))
3imtr3d.3 (φ → (χτ))
Assertion
Ref Expression
3imtr3d (φ → (θτ))

Proof of Theorem 3imtr3d
StepHypRef Expression
1 3imtr3d.2 . 2 (φ → (ψθ))
2 3imtr3d.1 . . 3 (φ → (ψχ))
3 3imtr3d.3 . . 3 (φ → (χτ))
42, 3sylibd 138 . 2 (φ → (ψτ))
51, 4sylbird 159 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:  f1imass  5354  fornex  5681  tposfn2  5819  eroveu  6126  indpi  6319
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