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Theorem syl3an3b 1525
Description: A syllogism inference. (Contributed by NM, 22-Aug-1995.)
Hypotheses
Ref Expression
syl3an3b.1 (𝜑𝜃)
syl3an3b.2 ((𝜓𝜒𝜃) → 𝜏)
Assertion
Ref Expression
syl3an3b ((𝜓𝜒𝜑) → 𝜏)

Proof of Theorem syl3an3b
StepHypRef Expression
1 syl3an3b.1 . . 3 (𝜑𝜃)
21biimpi 208 . 2 (𝜑𝜃)
3 syl3an3b.2 . 2 ((𝜓𝜒𝜃) → 𝜏)
42, 3syl3an3 1206 1 ((𝜓𝜒𝜑) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 198  w3a 1108
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 199  df-an 386  df-3an 1110
This theorem is referenced by:  fresaunres1  6292  fvun2  6495  nnmsucr  7945  xrlttr  12220  iccdil  12564  icccntr  12566  absexpz  14386  posglbd  17465  f1omvdco3  18181  isdrngd  19090  unicld  21179  2ndcdisj2  21589  logrec  24845  cdj3lem3  29822  bnj563  31330  bnj1033  31554  stoweidlem14  40974
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