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Theorem ssuni 4273
 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 2540 . . . . . . 7
21imbi1d 317 . . . . . 6
3 elunii 4256 . . . . . . 7
43expcom 435 . . . . . 6
52, 4vtoclga 3182 . . . . 5
65imim2d 52 . . . 4
76alimdv 1685 . . 3
8 dfss2 3498 . . 3
9 dfss2 3498 . . 3
107, 8, 93imtr4g 270 . 2
1110impcom 430 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369  wal 1377   wceq 1379   wcel 1767   wss 3481  cuni 4251 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-v 3120  df-in 3488  df-ss 3495  df-uni 4252 This theorem is referenced by:  elssuni  4281  uniss2  4284  ssorduni  6616  filssufilg  20280  alexsubALTlem2  20416  utoptop  20605  locfinreflem  27668
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