Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  opabss Unicode version

Theorem opabss 3821
 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 3819 . 2
2 df-br 3765 . . . . 5
3 eleq1 2100 . . . . . 6
43biimpar 281 . . . . 5
52, 4sylan2b 271 . . . 4
65exlimivv 1776 . . 3
76abssi 3015 . 2
81, 7eqsstri 2975 1
 Colors of variables: wff set class Syntax hints:   wa 97   wceq 1243  wex 1381   wcel 1393  cab 2026   wss 2917  cop 3378   class class class wbr 3764  copab 3817 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-in 2924  df-ss 2931  df-br 3765  df-opab 3819 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator