Theorem ssintab 4303

Description: Subclass of the intersection of a class abstraction. (Contributed by NM, 31-Jul-2006.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)

Assertion

Ref	Expression
ssintab

Distinct variable group:   ,

Proof of Theorem ssintab

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		ssint 4302	. 2
2		sseq2 3525	. . 3
3	2	ralab2 3264	. 2
4	1, 3	bitri 249	1

Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  {cab 2442  A.wral 2807  C_wss 3475  |^|cint 4286

This theorem is referenced by:  ssmin  4305  ssintrab  4310  intmin4  4316  dffi2  7903  rankval3b  8265  sstskm  9241  dfuzi  10978  cycsubg  16229  ssmclslem  28925

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-or 370  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-nfc 2607  df-ral 2812  df-v 3111  df-in 3482  df-ss 3489  df-int 4287