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Theorem sylibd 205
Description: A syllogism deduction. (Contributed by NM, 3-Aug-1994.)
Hypotheses
Ref Expression
sylibd.1 (φ → (ψχ))
sylibd.2 (φ → (χθ))
Assertion
Ref Expression
sylibd (φ → (ψθ))

Proof of Theorem sylibd
StepHypRef Expression
1 sylibd.1 . 2 (φ → (ψχ))
2 sylibd.2 . . 3 (φ → (χθ))
32biimpd 198 . 2 (φ → (χθ))
41, 3syld 40 1 (φ → (ψθ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177
This theorem is referenced by:  3imtr3d  258  ceqsalt  2882  sbceqal  3098  sbcimdv  3108  csbiebt  3173  rspcsbela  3196  ltfintri  4467  copsexg  4608  fce  6189  spacind  6288
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