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Theorem sylan9ssr 3978
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 3977 . 2 ((𝜑𝜓) → 𝐴𝐶)
43ancoms 459 1 ((𝜓𝜑) → 𝐴𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  wss 3933
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-in 3940  df-ss 3949
This theorem is referenced by:  intssuni2  4892  marypha1  8886  cardinfima  9511  cfflb  9669  ssfin4  9720  acsfn  16918  mrelatlub  17784  efgval  18772  islbs3  19856  kgentopon  22074  txlly  22172  sigaclci  31290  bnj1014  32131  topjoin  33610  filnetlem3  33625  poimirlem16  34789  mblfinlem3  34812  sspwimpALT  41136  sspwimpALT2  41139  setrecsres  44732
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