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Theorem ssuni 3602
 Description: Subclass relationship for class union. (Contributed by NM, 24-May-1994.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
ssuni

Proof of Theorem ssuni
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eleq2 2101 . . . . . . 7
21imbi1d 220 . . . . . 6
3 elunii 3585 . . . . . . 7
43expcom 109 . . . . . 6
52, 4vtoclga 2619 . . . . 5
65imim2d 48 . . . 4
76alimdv 1759 . . 3
8 dfss2 2934 . . 3
9 dfss2 2934 . . 3
107, 8, 93imtr4g 194 . 2
1110impcom 116 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97  wal 1241   wceq 1243   wcel 1393   wss 2917  cuni 3580 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-in 2924  df-ss 2931  df-uni 3581 This theorem is referenced by:  elssuni  3608  uniss2  3611  ssorduni  4213
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