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Theorem sylanr2 682
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 618 . 2 ((𝜒𝜑) → (𝜒𝜃))
3 sylanr2.2 . 2 ((𝜓 ∧ (𝜒𝜃)) → 𝜏)
42, 3sylan2 594 1 ((𝜓 ∧ (𝜒𝜑)) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 397
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 398
This theorem is referenced by:  adantrrl  723  adantrrr  724  unfi  9172  isfin7-2  10391  mulsub  11657  fzsubel  13537  expsub  14076  ramlb  16952  0ram  16953  ressmplvsca  21586  tgcl  22472  fgss2  23378  nmoid  24259  madebdaylemlrcut  27394  numclwwlkqhash  29659  chirredlem4  31677  pibt2  36346  lindsadd  36529  poimirlem28  36564  pridlc3  36989  stoweidlem34  44798
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