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| Mirrors > Home > ILE Home > Th. List > opabssxp | Unicode version | ||
| Description: An abstraction relation is a subset of a related cross product. (Contributed by NM, 16-Jul-1995.) |
| Ref | Expression |
|---|---|
| opabssxp |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | simpl 109 |
. . 3
| |
| 2 | 1 | ssopab2i 4323 |
. 2
|
| 3 | df-xp 4680 |
. 2
| |
| 4 | 2, 3 | sseqtrri 3227 |
1
|
| Colors of variables: wff set class |
| Syntax hints: |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1469 ax-7 1470 ax-gen 1471 ax-ie1 1515 ax-ie2 1516 ax-8 1526 ax-10 1527 ax-11 1528 ax-i12 1529 ax-bndl 1531 ax-4 1532 ax-17 1548 ax-i9 1552 ax-ial 1556 ax-i5r 1557 ax-ext 2186 |
| This theorem depends on definitions: df-bi 117 df-nf 1483 df-sb 1785 df-clab 2191 df-cleq 2197 df-clel 2200 df-nfc 2336 df-in 3171 df-ss 3178 df-opab 4105 df-xp 4680 |
| This theorem is referenced by: brab2ga 4749 dmoprabss 6026 ecopovsym 6717 ecopovtrn 6718 ecopover 6719 ecopovsymg 6720 ecopovtrng 6721 ecopoverg 6722 opabfi 7034 netap 7365 2omotaplemap 7368 2omotaplemst 7369 enqex 7472 ltrelnq 7477 enq0ex 7551 ltrelpr 7617 enrex 7849 ltrelsr 7850 ltrelre 7945 ltrelxr 8132 dvdszrcl 12074 prdsex 13072 prdsval 13076 prdsbaslemss 13077 releqgg 13527 eqgex 13528 aprval 14015 aprap 14019 lmfval 14635 lgsquadlemofi 15524 lgsquadlem1 15525 lgsquadlem2 15526 |
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