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Theorem sylanbr 269
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 124 . 2 (φψ)
3 sylanbr.2 . 2 ((ψ χ) → θ)
42, 3sylan 267 1 ((φ χ) → θ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  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:  syl2anbr  276  mosubt  2691  xpiindim  4396  funfvdm  5157  caovimo  5613  tfrlem7  5851  iinerm  6085
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