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Theorem supeu 7462
 Description: A supremum is unique. Similar to Theorem I.26 of [Apostol] p. 24 (but for suprema in general). (Contributed by NM, 12-Oct-2004.)
Hypotheses
Ref Expression
supmo.1
supeu.2
Assertion
Ref Expression
supeu
Distinct variable groups:   ,,,   ,,,   ,,,
Allowed substitution hints:   (,,)

Proof of Theorem supeu
StepHypRef Expression
1 supeu.2 . 2
2 supmo.1 . . 3
32supmo 7460 . 2
4 reu5 2923 . 2
51, 3, 4sylanbrc 647 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 360  wral 2707  wrex 2708  wreu 2709  wrmo 2710   class class class wbr 4215   wor 4505 This theorem is referenced by:  supval2  7463  eqsup  7464  supcl  7466  supub  7467  suplub  7468  fisup2g  7474  fisupcl  7475 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-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 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-ral 2712  df-rex 2713  df-reu 2714  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-br 4216  df-po 4506  df-so 4507
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