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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 4377 | . . 3 | |
2 | 1 | ineq2d 3167 | . 2 |
3 | df-res 4375 | . 2 | |
4 | df-res 4375 | . 2 | |
5 | 2, 3, 4 | 3eqtr4g 2138 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1284 cvv 2601 cin 2972 cxp 4361 cres 4365 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 df-in 2979 df-opab 3840 df-xp 4369 df-res 4375 |
This theorem is referenced by: reseq2i 4627 reseq2d 4630 resabs1 4658 resima2 4662 imaeq2 4684 resdisj 4771 relcoi1 4869 fressnfv 5371 tfrlem1 5946 tfrlem9 5958 tfr0 5960 tfrlemisucaccv 5962 tfrlemiubacc 5967 fnfi 6388 |
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