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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 109 |
. . 3
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2 | 1 | ssopab2i 4276 |
. 2
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3 | df-xp 4631 |
. 2
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4 | 2, 3 | sseqtrri 3190 |
1
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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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-in 3135 df-ss 3142 df-opab 4064 df-xp 4631 |
This theorem is referenced by: brab2ga 4700 dmoprabss 5954 ecopovsym 6628 ecopovtrn 6629 ecopover 6630 ecopovsymg 6631 ecopovtrng 6632 ecopoverg 6633 netap 7250 2omotaplemap 7253 2omotaplemst 7254 enqex 7356 ltrelnq 7361 enq0ex 7435 ltrelpr 7501 enrex 7733 ltrelsr 7734 ltrelre 7829 ltrelxr 8014 dvdszrcl 11792 releqgg 13011 aprval 13271 aprap 13275 lmfval 13563 |
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