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Theorem syl3an2br 1222
Description: A syllogism inference. (Contributed by NM, 22-Aug-1995.)
Hypotheses
Ref Expression
syl3an2br.1 (χφ)
syl3an2br.2 ((ψ χ θ) → τ)
Assertion
Ref Expression
syl3an2br ((ψ φ θ) → τ)

Proof of Theorem syl3an2br
StepHypRef Expression
1 syl3an2br.1 . . 3 (χφ)
21biimpri 197 . 2 (φχ)
3 syl3an2br.2 . 2 ((ψ χ θ) → τ)
42, 3syl3an2 1216 1 ((ψ φ θ) → τ)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   w3a 934
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  df-3an 936
This theorem is referenced by: (None)
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