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Theorem iinss2 4351
 Description: An indexed intersection is included in any of its members. (Contributed by FL, 15-Oct-2012.)
Assertion
Ref Expression
iinss2

Proof of Theorem iinss2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 vex 3083 . . . . 5
2 eliin 4305 . . . . 5
31, 2ax-mp 5 . . . 4
4 rsp 2788 . . . 4
53, 4sylbi 198 . . 3
65com12 32 . 2
76ssrdv 3470 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wcel 1872  wral 2771  cvv 3080   wss 3436  ciin 4300 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-ral 2776  df-v 3082  df-in 3443  df-ss 3450  df-iin 4302 This theorem is referenced by:  dmiin  5097  gruiin  9242  txtube  20653
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