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Theorem opabssxp 4414
 Description: An abstraction relation is a subset of a related cross product. (Contributed by NM, 16-Jul-1995.)
Assertion
Ref Expression
opabssxp
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem opabssxp
StepHypRef Expression
1 simpl 102 . . 3
21ssopab2i 4014 . 2
3 df-xp 4351 . 2
42, 3sseqtr4i 2978 1
 Colors of variables: wff set class Syntax hints:   wa 97   wcel 1393   wss 2917  copab 3817   cxp 4343 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-opab 3819  df-xp 4351 This theorem is referenced by:  brab2ga  4415  dmoprabss  5586  ecopovsym  6202  ecopovtrn  6203  ecopover  6204  ecopovsymg  6205  ecopovtrng  6206  ecopoverg  6207  enqex  6458  ltrelnq  6463  enq0ex  6537  ltrelpr  6603  enrex  6822  ltrelsr  6823  ltrelre  6909  ltrelxr  7080
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