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Theorem ssuni 4038
 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 2498 . . . . . . 7
21imbi1d 310 . . . . . 6
3 elunii 4021 . . . . . . 7
43expcom 426 . . . . . 6
52, 4vtoclga 3018 . . . . 5
65imim2d 51 . . . 4
76alimdv 1632 . . 3
8 dfss2 3338 . . 3
9 dfss2 3338 . . 3
107, 8, 93imtr4g 263 . 2
1110impcom 421 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360  wal 1550   wceq 1653   wcel 1726   wss 3321  cuni 4016 This theorem is referenced by:  elssuni  4044  uniss2  4047  ssorduni  4767  filssufilg  17944  alexsubALTlem2  18080  utoptop  18265 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-v 2959  df-in 3328  df-ss 3335  df-uni 4017
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