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Theorem sylanr2 683
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 617 . 2 ((𝜒𝜑) → (𝜒𝜃))
3 sylanr2.2 . 2 ((𝜓 ∧ (𝜒𝜃)) → 𝜏)
42, 3sylan2 593 1 ((𝜓 ∧ (𝜒𝜑)) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395
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 207  df-an 396
This theorem is referenced by:  adantrrl  724  adantrrr  725  unfi  9211  isfin7-2  10436  mulsub  11706  fzsubel  13600  expsub  14151  ramlb  17057  0ram  17058  ressmplvsca  22049  tgcl  22976  fgss2  23882  nmoid  24763  madebdaylemlrcut  27937  numclwwlkqhash  30394  chirredlem4  32412  pibt2  37418  lindsadd  37620  poimirlem28  37655  pridlc3  38080  stoweidlem34  46049
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