Theorem sylan9ss 3516

Description: A subclass transitivity deduction. (Contributed by NM, 27-Sep-2004.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)

Hypotheses

Ref	Expression
sylan9ss.1
sylan9ss.2

Assertion

Ref	Expression
sylan9ss

Proof of Theorem sylan9ss

Step	Hyp	Ref	Expression
1		sylan9ss.1	. 2
2		sylan9ss.2	. 2
3		sstr 3511	. 2
4	1, 2, 3	syl2an 477	1

Syntax hints:  ->wi 4  /\wa 369  C_wss 3475

This theorem is referenced by:  sylan9ssr  3517  psstr  3607  unss12  3675  ss2in  3724  relrelss  5536  funssxp  5749  axdc3lem  8851  tskuni  9182  tsmsxp  20657  shslubi  26303  chlej12i  26393  insiga  28137  rtrclreclem.min  29070  fnetr  30169  pcl0bN  35647

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-in 3482  df-ss 3489