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Theorem supexd 7625
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 7613 . 2
2 supmo.1 . . . 4
32supmo 7624 . . 3
4 rmorabex 4575 . . 3
5 uniexg 6387 . . 3
63, 4, 53syl 19 . 2
71, 6syl5eqel 2573 1
Colors of variables: wff set class
Syntax hints:  -.wn 3  ->wi 4  /\wa 360  e.wcel 1732  A.wral 2759  E.wrex 2760  E*wrmo 2762  {crab 2763   cvv 3015  U.cuni 4117   class class class wbr 4318  Orwor 4661  supcsup 7612
This theorem is referenced by:  supex  7635  wsucex  26916
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1570  ax-4 1581  ax-5 1644  ax-6 1685  ax-7 1705  ax-8 1734  ax-9 1736  ax-10 1751  ax-11 1756  ax-12 1768  ax-13 1955  ax-ext 2470  ax-sep 4439  ax-nul 4447  ax-pr 4554  ax-un 6382
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 940  df-3an 941  df-tru 1338  df-ex 1566  df-nf 1569  df-sb 1677  df-eu 2317  df-mo 2318  df-clab 2476  df-cleq 2482  df-clel 2485  df-nfc 2614  df-ne 2654  df-ral 2764  df-rex 2765  df-rmo 2767  df-rab 2768  df-v 3017  df-dif 3368  df-un 3370  df-in 3372  df-ss 3379  df-nul 3674  df-if 3826  df-sn 3915  df-pr 3916  df-op 3918  df-uni 4118  df-br 4319  df-po 4662  df-so 4663  df-sup 7613
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