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Theorem sylanr2 681
Description: A syllogism inference. (Contributed by NM, 9-Apr-2005.)
Hypotheses
Ref Expression
sylanr2.1 (𝜑𝜃)
sylanr2.2 ((𝜓 ∧ (𝜒𝜃)) → 𝜏)
Assertion
Ref Expression
sylanr2 ((𝜓 ∧ (𝜒𝜑)) → 𝜏)

Proof of Theorem sylanr2
StepHypRef Expression
1 sylanr2.1 . . 3 (𝜑𝜃)
21anim2i 615 . 2 ((𝜒𝜑) → (𝜒𝜃))
3 sylanr2.2 . 2 ((𝜓 ∧ (𝜒𝜃)) → 𝜏)
42, 3sylan2 591 1 ((𝜓 ∧ (𝜒𝜑)) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 394
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 206  df-an 395
This theorem is referenced by:  adantrrl  722  adantrrr  723  unfi  9197  isfin7-2  10421  mulsub  11689  fzsubel  13572  expsub  14111  ramlb  16991  0ram  16992  ressmplvsca  21991  tgcl  22916  fgss2  23822  nmoid  24703  madebdaylemlrcut  27871  numclwwlkqhash  30257  chirredlem4  32275  pibt2  37027  lindsadd  37217  poimirlem28  37252  pridlc3  37677  stoweidlem34  45560
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