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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | resopab2 4836 | . 2 | |
2 | df-mpt 3961 | . . 3 | |
3 | 2 | reseq1i 4785 | . 2 |
4 | df-mpt 3961 | . 2 | |
5 | 1, 3, 4 | 3eqtr4g 2175 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1316 wcel 1465 wss 3041 copab 3958 cmpt 3959 cres 4511 |
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-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-opab 3960 df-mpt 3961 df-xp 4515 df-rel 4516 df-res 4521 |
This theorem is referenced by: resmpt3 4838 resmptf 4839 resmptd 4840 f1stres 6025 f2ndres 6026 tposss 6111 dftpos2 6126 dftpos4 6128 djuf1olemr 6907 fisumss 11129 isumclim3 11160 expcnv 11241 tgrest 12265 cnmptid 12377 dvidlemap 12756 dvcnp2cntop 12759 dvmulxxbr 12762 dvcoapbr 12767 dvrecap 12773 |
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