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Theorem sylan2br 272
Description: A syllogism inference. (Contributed by NM, 21-Apr-1994.)
Hypotheses
Ref Expression
sylan2br.1 (χφ)
sylan2br.2 ((ψ χ) → θ)
Assertion
Ref Expression
sylan2br ((ψ φ) → θ)

Proof of Theorem sylan2br
StepHypRef Expression
1 sylan2br.1 . . 3 (χφ)
21biimpri 124 . 2 (φχ)
3 sylan2br.2 . 2 ((ψ χ) → θ)
42, 3sylan2 270 1 ((ψ φ) → 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  xordc1  1267  imainss  4666  xpexr2m  4689  funeu2  4853  imadiflem  4904  fnop  4928  ssimaex  5159  isosolem  5388  acexmidlem2  5433  fnovex  5462  smores3  5830  riinerm  6090  enq0sym  6287
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