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Theorem sylbird 159
Description: A syllogism deduction. (Contributed by NM, 3-Aug-1994.)
Hypotheses
Ref Expression
sylbird.1 (φ → (χψ))
sylbird.2 (φ → (χθ))
Assertion
Ref Expression
sylbird (φ → (ψθ))

Proof of Theorem sylbird
StepHypRef Expression
1 sylbird.1 . . 3 (φ → (χψ))
21biimprd 147 . 2 (φ → (ψχ))
3 sylbird.2 . 2 (φ → (χθ))
42, 3syld 40 1 (φ → (ψθ))
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:  3imtr3d  191  drex1  1661  eqreu  2710  onsucsssucr  4184  ordsucunielexmid  4200  ovi3  5560  tfrlem9  5857  rdgon  5893  distrlem4prl  6423  distrlem4pru  6424  recexprlemm  6458  renegcl  6858
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