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Mirrors > Home > ILE Home > Th. List > resmpt | Unicode version |
Description: Restriction of the mapping operation. (Contributed by Mario Carneiro, 15-Jul-2013.) |
Ref | Expression |
---|---|
resmpt |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | resopab2 4874 |
. 2
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2 | df-mpt 3999 |
. . 3
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3 | 2 | reseq1i 4823 |
. 2
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4 | df-mpt 3999 |
. 2
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5 | 1, 3, 4 | 3eqtr4g 2198 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-opab 3998 df-mpt 3999 df-xp 4553 df-rel 4554 df-res 4559 |
This theorem is referenced by: resmpt3 4876 resmptf 4877 resmptd 4878 f1stres 6065 f2ndres 6066 tposss 6151 dftpos2 6166 dftpos4 6168 djuf1olemr 6947 fisumss 11193 isumclim3 11224 expcnv 11305 tgrest 12377 cnmptid 12489 dvidlemap 12868 dvcnp2cntop 12871 dvmulxxbr 12874 dvcoapbr 12879 dvrecap 12885 |
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