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Theorem supexd 7461
 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 7449 . 2
2 supmo.1 . . . 4
32supmo 7460 . . 3
4 rmorabex 4426 . . 3
5 uniexg 4709 . . 3
63, 4, 53syl 19 . 2
71, 6syl5eqel 2522 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 360   wcel 1726  wral 2707  wrex 2708  wrmo 2710  crab 2711  cvv 2958  cuni 4017   class class class wbr 4215   wor 4505  csup 7448 This theorem is referenced by:  supex  7471  wsucex  25582 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 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406  ax-un 4704 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 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rmo 2715  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4216  df-po 4506  df-so 4507  df-sup 7449
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