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Theorem syl2an3an 1531
 Description: syl3an 1162 with antecedents in standard conjunction form. (Contributed by Alan Sare, 31-Aug-2016.)
Hypotheses
Ref Expression
syl2an3an.1 (𝜑𝜓)
syl2an3an.2 (𝜑𝜒)
syl2an3an.3 (𝜃𝜏)
syl2an3an.4 ((𝜓𝜒𝜏) → 𝜂)
Assertion
Ref Expression
syl2an3an ((𝜑𝜃) → 𝜂)

Proof of Theorem syl2an3an
StepHypRef Expression
1 syl2an3an.1 . . 3 (𝜑𝜓)
2 syl2an3an.2 . . 3 (𝜑𝜒)
3 syl2an3an.3 . . 3 (𝜃𝜏)
4 syl2an3an.4 . . 3 ((𝜓𝜒𝜏) → 𝜂)
51, 2, 3, 4syl3an 1162 . 2 ((𝜑𝜑𝜃) → 𝜂)
653anidm12 1528 1 ((𝜑𝜃) → 𝜂)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 382   ∧ w3a 1070 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 197  df-an 383  df-3an 1072 This theorem is referenced by:  syl2an23an  1532  disjxiun  4781  funcnvtp  6092  cncongr1  15587  gausslemma2dlem2  25312  eucrctshift  27420  numclwlk1lem1  27555  fmtnofac2lem  41998
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