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Theorem sylani 635
Description: A syllogism inference. (Contributed by NM, 2-May-1996.)
Hypotheses
Ref Expression
sylani.1 (φχ)
sylani.2 (ψ → ((χ θ) → τ))
Assertion
Ref Expression
sylani (ψ → ((φ θ) → τ))

Proof of Theorem sylani
StepHypRef Expression
1 sylani.1 . . 3 (φχ)
21a1i 10 . 2 (ψ → (φχ))
3 sylani.2 . 2 (ψ → ((χ θ) → τ))
42, 3syland 467 1 (ψ → ((φ θ) → τ))
Colors of variables: wff setvar class
Syntax hints:  wi 4   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:  syl2ani  637
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