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Theorem opabss 4513
 Description: The collection of ordered pairs in a class is a subclass of it. (Contributed by NM, 27-Dec-1996.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)
Assertion
Ref Expression
opabss
Distinct variable groups:   ,   ,

Proof of Theorem opabss
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-opab 4511 . 2
2 df-br 4453 . . . . 5
3 eleq1 2529 . . . . . 6
43biimpar 485 . . . . 5
52, 4sylan2b 475 . . . 4
65exlimivv 1723 . . 3
76abssi 3574 . 2
81, 7eqsstri 3533 1
 Colors of variables: wff setvar class Syntax hints:  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818  {cab 2442  C_wss 3475  <.cop 4035   class class class wbr 4452  {copab 4509 This theorem is referenced by:  aceq3lem  8522  fullfunc  15275  fthfunc  15276  isfull  15279  isfth  15283 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-in 3482  df-ss 3489  df-br 4453  df-opab 4511
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