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Theorem ssiun 4372
 Description: Subset implication for an indexed union. (Contributed by NM, 3-Sep-2003.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)
Assertion
Ref Expression
ssiun
Distinct variable group:   ,

Proof of Theorem ssiun
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ssel 3497 . . . . 5
21reximi 2925 . . . 4
3 r19.37v 3007 . . . 4
42, 3syl 16 . . 3
5 eliun 4335 . . 3
64, 5syl6ibr 227 . 2
76ssrdv 3509 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  e.wcel 1818  E.wrex 2808  C_wss 3475  U_ciun 4330 This theorem is referenced by:  iunss2  4375  iunpwss  4420  iunpw  6614  onfununi  7031  oen0  7254  trcl  8180  rtrclreclem.refl  29067  rtrclreclem.subset  29068  trpredtr  29313  dftrpred3g  29316  wfrlem9  29351  frrlem5e  29395 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-nfc 2607  df-ral 2812  df-rex 2813  df-v 3111  df-in 3482  df-ss 3489  df-iun 4332
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