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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 108 | . . 3 | |
2 | 1 | ssopab2i 4199 | . 2 |
3 | df-xp 4545 | . 2 | |
4 | 2, 3 | sseqtrri 3132 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wcel 1480 wss 3071 copab 3988 cxp 4537 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-in 3077 df-ss 3084 df-opab 3990 df-xp 4545 |
This theorem is referenced by: brab2ga 4614 dmoprabss 5853 ecopovsym 6525 ecopovtrn 6526 ecopover 6527 ecopovsymg 6528 ecopovtrng 6529 ecopoverg 6530 enqex 7168 ltrelnq 7173 enq0ex 7247 ltrelpr 7313 enrex 7545 ltrelsr 7546 ltrelre 7641 ltrelxr 7825 dvdszrcl 11498 lmfval 12361 |
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