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Theorem supexd 7507
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 7495 . 2
2 supmo.1 . . . 4
32supmo 7506 . . 3
4 rmorabex 4462 . . 3
5 uniexg 4747 . . 3
63, 4, 53syl 19 . 2
71, 6syl5eqel 2527 1
Colors of variables: wff set class
Syntax hints:  -.wn 3  ->wi 4  /\wa 360  e.wcel 1728  A.wral 2712  E.wrex 2713  E*wrmo 2715  {crab 2716   cvv 2965  U.cuni 4043   class class class wbr 4243  Orwor 4543  supcsup 7494
This theorem is referenced by:  supex  7517  wsucex  25681
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-13 1730  ax-14 1732  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424  ax-sep 4364  ax-nul 4372  ax-pr 4442  ax-un 4742
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 938  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-eu 2292  df-mo 2293  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-ne 2608  df-ral 2717  df-rex 2718  df-rmo 2720  df-rab 2721  df-v 2967  df-dif 3312  df-un 3314  df-in 3316  df-ss 3323  df-nul 3617  df-if 3766  df-sn 3847  df-pr 3848  df-op 3850  df-uni 4044  df-br 4244  df-po 4544  df-so 4545  df-sup 7495
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