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Theorem reusn 3793
Description: A way to express restricted existential uniqueness of a wff: its restricted class abstraction is a singleton. (Contributed by NM, 30-May-2006.) (Proof shortened by Mario Carneiro, 14-Nov-2016.)
Assertion
Ref Expression
reusn
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem reusn
StepHypRef Expression
1 euabsn2 3791 . 2
2 df-reu 2621 . 2
3 df-rab 2623 . . . 4
43eqeq1i 2360 . . 3
54exbii 1582 . 2
61, 2, 53bitr4i 268 1
Colors of variables: wff setvar class
Syntax hints:   wb 176   wa 358  wex 1541   wceq 1642   wcel 1710  weu 2204  cab 2339  wreu 2616  crab 2618  csn 3737
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-clab 2340  df-cleq 2346  df-clel 2349  df-reu 2621  df-rab 2623  df-sn 3741
This theorem is referenced by: (None)
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