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Theorem ssiin 4380
Description: Subset theorem for an indexed intersection. (Contributed by NM, 15-Oct-2003.)
Assertion
Ref Expression
ssiin
Distinct variable group:   ,

Proof of Theorem ssiin
StepHypRef Expression
1 nfcv 2619 . 2
21ssiinf 4379 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  A.wral 2807  C_wss 3475  |^|_ciin 4331
This theorem is referenced by:  cflim2  8664  ptbasfi  20082  limciun  22298  clsint2  30147  fnemeet2  30185  dihglblem4  37024  dihglblem6  37067
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-iin 4333
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