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Theorem supexd 7933
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 7921 . 2
2 supmo.1 . . . 4
32supmo 7932 . . 3
4 rmorabex 4712 . . 3
5 uniexg 6597 . . 3
63, 4, 53syl 20 . 2
71, 6syl5eqel 2549 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  /\wa 369  e.wcel 1818  A.wral 2807  E.wrex 2808  E*wrmo 2810  {crab 2811   cvv 3109  U.cuni 4249   class class class wbr 4452  Orwor 4804  supcsup 7920
This theorem is referenced by:  supex  7943  omsfval  28265  wsucex  29382
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691  ax-un 6592
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rmo 2815  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-po 4805  df-so 4806  df-sup 7921
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