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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 4866 | . 2 | |
2 | df-mpt 3991 | . . 3 | |
3 | 2 | reseq1i 4815 | . 2 |
4 | df-mpt 3991 | . 2 | |
5 | 1, 3, 4 | 3eqtr4g 2197 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1331 wcel 1480 wss 3071 copab 3988 cmpt 3989 cres 4541 |
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-opab 3990 df-mpt 3991 df-xp 4545 df-rel 4546 df-res 4551 |
This theorem is referenced by: resmpt3 4868 resmptf 4869 resmptd 4870 f1stres 6057 f2ndres 6058 tposss 6143 dftpos2 6158 dftpos4 6160 djuf1olemr 6939 fisumss 11161 isumclim3 11192 expcnv 11273 tgrest 12338 cnmptid 12450 dvidlemap 12829 dvcnp2cntop 12832 dvmulxxbr 12835 dvcoapbr 12840 dvrecap 12846 |
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