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Mirrors > Home > ILE Home > Th. List > reseq2 | Unicode version |
Description: Equality theorem for restrictions. (Contributed by NM, 8-Aug-1994.) |
Ref | Expression |
---|---|
reseq2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xpeq1 4612 | . . 3 | |
2 | 1 | ineq2d 3318 | . 2 |
3 | df-res 4610 | . 2 | |
4 | df-res 4610 | . 2 | |
5 | 2, 3, 4 | 3eqtr4g 2222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1342 cvv 2721 cin 3110 cxp 4596 cres 4600 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-in 3117 df-opab 4038 df-xp 4604 df-res 4610 |
This theorem is referenced by: reseq2i 4875 reseq2d 4878 resabs1 4907 resima2 4912 imaeq2 4936 resdisj 5026 relcoi1 5129 fressnfv 5666 tfrlem1 6267 tfrlem9 6278 tfr0dm 6281 tfrlemisucaccv 6284 tfrlemiubacc 6289 tfr1onlemsucaccv 6300 tfr1onlemubacc 6305 tfr1onlemaccex 6307 tfrcllemsucaccv 6313 tfrcllembxssdm 6315 tfrcllemubacc 6318 tfrcllemaccex 6320 tfrcllemres 6321 tfrcldm 6322 fnfi 6893 lmbr2 12761 lmff 12796 |
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