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Theorem sylan9ssr 3997
Description: A subclass transitivity deduction. (Contributed by NM, 27-Sep-2004.)
Hypotheses
Ref Expression
sylan9ssr.1 (𝜑𝐴𝐵)
sylan9ssr.2 (𝜓𝐵𝐶)
Assertion
Ref Expression
sylan9ssr ((𝜓𝜑) → 𝐴𝐶)

Proof of Theorem sylan9ssr
StepHypRef Expression
1 sylan9ssr.1 . . 3 (𝜑𝐴𝐵)
2 sylan9ssr.2 . . 3 (𝜓𝐵𝐶)
31, 2sylan9ss 3996 . 2 ((𝜑𝜓) → 𝐴𝐶)
43ancoms 460 1 ((𝜓𝜑) → 𝐴𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 397  wss 3949
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-in 3956  df-ss 3966
This theorem is referenced by:  intssuni2  4978  marypha1  9429  cardinfima  10092  cfflb  10254  ssfin4  10305  acsfn  17603  mrelatlub  18515  efgval  19585  islbs3  20768  kgentopon  23042  txlly  23140  sigaclci  33130  bnj1014  33972  topjoin  35250  filnetlem3  35265  poimirlem16  36504  mblfinlem3  36527  sspwimpALT  43686  sspwimpALT2  43689  setrecsres  47747
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