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Theorem ssequn1 3246
 Description: A relationship between subclass and union. Theorem 26 of [Suppes] p. 27. (Contributed by NM, 30-Aug-1993.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
ssequn1

Proof of Theorem ssequn1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bicom 139 . . . 4
2 pm4.72 812 . . . 4
3 elun 3217 . . . . 5
43bibi1i 227 . . . 4
51, 2, 43bitr4i 211 . . 3
65albii 1446 . 2
7 dfss2 3086 . 2
8 dfcleq 2133 . 2
96, 7, 83bitr4i 211 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wo 697  wal 1329   wceq 1331   wcel 1480   cun 3069   wss 3071 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-in 3077  df-ss 3084 This theorem is referenced by:  ssequn2  3249  uniop  4177  pwssunim  4206  unisuc  4335  unisucg  4336  rdgisucinc  6282  oasuc  6360  omsuc  6368  undifdc  6812
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