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Theorem sylan9ssr 3650
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 3649 . 2 ((𝜑𝜓) → 𝐴𝐶)
43ancoms 468 1 ((𝜓𝜑) → 𝐴𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  wss 3607
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-in 3614  df-ss 3621
This theorem is referenced by:  intssuni2  4534  marypha1  8381  cardinfima  8958  cfflb  9119  ssfin4  9170  acsfn  16367  mrelatlub  17233  efgval  18176  islbs3  19203  kgentopon  21389  txlly  21487  sigaclci  30323  bnj1014  31156  topjoin  32485  filnetlem3  32500  poimirlem16  33555  mblfinlem3  33578  sspwimpALT  39475  sspwimpALT2  39478  setrecsres  42773
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