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Mirrors > Home > ILE Home > Th. List > ovres | Unicode version |
Description: The value of a restricted operation. (Contributed by FL, 10-Nov-2006.) |
Ref | Expression |
---|---|
ovres |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelxpi 4641 | . . 3 | |
2 | fvres 5518 | . . 3 | |
3 | 1, 2 | syl 14 | . 2 |
4 | df-ov 5854 | . 2 | |
5 | df-ov 5854 | . 2 | |
6 | 3, 4, 5 | 3eqtr4g 2228 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 wcel 2141 cop 3584 cxp 4607 cres 4611 cfv 5196 (class class class)co 5851 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4105 ax-pow 4158 ax-pr 4192 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-pw 3566 df-sn 3587 df-pr 3588 df-op 3590 df-uni 3795 df-br 3988 df-opab 4049 df-xp 4615 df-res 4621 df-iota 5158 df-fv 5204 df-ov 5854 |
This theorem is referenced by: ovresd 5991 oprssov 5992 ofmresval 6070 elq 9570 mgmsscl 12604 xmetres2 13134 blres 13189 xmetresbl 13195 mscl 13220 xmscl 13221 xmsge0 13222 xmseq0 13223 divcnap 13310 cncfmet 13334 |
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