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Theorem sylan9ssr 3348
Description: A subclass transitivity deduction. (Contributed by NM, 27-Sep-2004.)
Hypotheses
Ref Expression
sylan9ssr.1  |-  ( ph  ->  A  C_  B )
sylan9ssr.2  |-  ( ps 
->  B  C_  C )
Assertion
Ref Expression
sylan9ssr  |-  ( ( ps  /\  ph )  ->  A  C_  C )

Proof of Theorem sylan9ssr
StepHypRef Expression
1 sylan9ssr.1 . . 3  |-  ( ph  ->  A  C_  B )
2 sylan9ssr.2 . . 3  |-  ( ps 
->  B  C_  C )
31, 2sylan9ss 3347 . 2  |-  ( (
ph  /\  ps )  ->  A  C_  C )
43ancoms 441 1  |-  ( ( ps  /\  ph )  ->  A  C_  C )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360    C_ wss 3306
This theorem is referenced by:  intssuni2  4099  marypha1  7468  cardinfima  8009  cfflb  8170  ssfin4  8221  acsfn  13915  mrelatlub  14643  efgval  15380  islbs3  16258  kgentopon  17601  txlly  17699  sigaclci  24546  mblfinlem3  26281  topjoin  26432  filnetlem3  26447  sspwimpALT  29135  sspwimpALT2  29138  bnj1014  29429
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-in 3313  df-ss 3320
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