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Theorem supexd 7946
 Description: A supremum is a set. (Contributed by NM, 22-May-1999.) (Revised by Mario Carneiro, 24-Dec-2016.)
Hypothesis
Ref Expression
supmo.1
Assertion
Ref Expression
supexd

Proof of Theorem supexd
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-sup 7935 . 2
2 supmo.1 . . . 4
32supmo 7945 . . 3
4 rmorabex 4651 . . 3
5 uniexg 6579 . . 3
63, 4, 53syl 18 . 2
71, 6syl5eqel 2494 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 367   wcel 1842  wral 2754  wrex 2755  wrmo 2757  crab 2758  cvv 3059  cuni 4191   class class class wbr 4395   wor 4743  csup 7934 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-8 1844  ax-9 1846  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380  ax-sep 4517  ax-nul 4525  ax-pr 4630  ax-un 6574 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3or 975  df-3an 976  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-eu 2242  df-mo 2243  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ne 2600  df-ral 2759  df-rex 2760  df-rmo 2762  df-rab 2763  df-v 3061  df-dif 3417  df-un 3419  df-in 3421  df-ss 3428  df-nul 3739  df-if 3886  df-sn 3973  df-pr 3975  df-op 3979  df-uni 4192  df-br 4396  df-po 4744  df-so 4745  df-sup 7935 This theorem is referenced by:  supex  7956  omsfval  28742  wsucex  30082
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