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Theorem sylanbr 459
Description: A syllogism inference. (Contributed by NM, 18-May-1994.)
Hypotheses
Ref Expression
sylanbr.1 (ψφ)
sylanbr.2 ((ψ χ) → θ)
Assertion
Ref Expression
sylanbr ((φ χ) → θ)

Proof of Theorem sylanbr
StepHypRef Expression
1 sylanbr.1 . . 3 (ψφ)
21biimpri 197 . 2 (φψ)
3 sylanbr.2 . 2 ((ψ χ) → θ)
42, 3sylan 457 1 ((φ χ) → θ)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   wa 358
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  df-an 360
This theorem is referenced by:  syl2anbr  466  funfv  5375
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