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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 4571 | . . 3 | |
2 | fvres 5445 | . . 3 | |
3 | 1, 2 | syl 14 | . 2 |
4 | df-ov 5777 | . 2 | |
5 | df-ov 5777 | . 2 | |
6 | 3, 4, 5 | 3eqtr4g 2197 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1331 wcel 1480 cop 3530 cxp 4537 cres 4541 cfv 5123 (class class class)co 5774 |
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-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-xp 4545 df-res 4551 df-iota 5088 df-fv 5131 df-ov 5777 |
This theorem is referenced by: ovresd 5911 oprssov 5912 ofmresval 5993 elq 9414 xmetres2 12548 blres 12603 xmetresbl 12609 mscl 12634 xmscl 12635 xmsge0 12636 xmseq0 12637 divcnap 12724 cncfmet 12748 |
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