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Theorem ssequn1 3113
 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 128 . . . 4
2 pm4.72 736 . . . 4
3 elun 3084 . . . . 5
43bibi1i 217 . . . 4
51, 2, 43bitr4i 201 . . 3
65albii 1359 . 2
7 dfss2 2934 . 2
8 dfcleq 2034 . 2
96, 7, 83bitr4i 201 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98   wo 629  wal 1241   wceq 1243   wcel 1393   cun 2915   wss 2917 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-in 2924  df-ss 2931 This theorem is referenced by:  ssequn2  3116  uniop  3992  pwssunim  4021  unisuc  4150  unisucg  4151  rdgisucinc  5972  oasuc  6044  omsuc  6051
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