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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 4169 | . 2 |
3 | df-xp 4515 | . 2 | |
4 | 2, 3 | sseqtrri 3102 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wcel 1465 wss 3041 copab 3958 cxp 4507 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-in 3047 df-ss 3054 df-opab 3960 df-xp 4515 |
This theorem is referenced by: brab2ga 4584 dmoprabss 5821 ecopovsym 6493 ecopovtrn 6494 ecopover 6495 ecopovsymg 6496 ecopovtrng 6497 ecopoverg 6498 enqex 7136 ltrelnq 7141 enq0ex 7215 ltrelpr 7281 enrex 7513 ltrelsr 7514 ltrelre 7609 ltrelxr 7793 dvdszrcl 11425 lmfval 12288 |
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