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Theorem opabss 4261
 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 4259 . 2
2 df-br 4205 . . . . 5
3 eleq1 2495 . . . . . 6
43biimpar 472 . . . . 5
52, 4sylan2b 462 . . . 4
65exlimivv 1645 . . 3
76abssi 3410 . 2
81, 7eqsstri 3370 1
 Colors of variables: wff set class Syntax hints:   wa 359  wex 1550   wceq 1652   wcel 1725  cab 2421   wss 3312  cop 3809   class class class wbr 4204  copab 4257 This theorem is referenced by:  aceq3lem  7993  fullfunc  14095  fthfunc  14096  isfull  14099  isfth  14103 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-in 3319  df-ss 3326  df-br 4205  df-opab 4259
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