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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 4914 | . 2 | |
2 | df-mpt 4028 | . . 3 | |
3 | 2 | reseq1i 4863 | . 2 |
4 | df-mpt 4028 | . 2 | |
5 | 1, 3, 4 | 3eqtr4g 2215 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1335 wcel 2128 wss 3102 copab 4025 cmpt 4026 cres 4589 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4083 ax-pow 4136 ax-pr 4170 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-opab 4027 df-mpt 4028 df-xp 4593 df-rel 4594 df-res 4599 |
This theorem is referenced by: resmpt3 4916 resmptf 4917 resmptd 4918 f1stres 6108 f2ndres 6109 tposss 6194 dftpos2 6209 dftpos4 6211 djuf1olemr 6999 fisumss 11293 isumclim3 11324 expcnv 11405 fprodssdc 11491 tgrest 12611 cnmptid 12723 dvidlemap 13102 dvcnp2cntop 13105 dvmulxxbr 13108 dvcoapbr 13113 dvrecap 13119 |
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