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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xpeq1 4658 |
. . 3
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2 | 1 | ineq2d 3351 |
. 2
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3 | df-res 4656 |
. 2
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4 | df-res 4656 |
. 2
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5 | 2, 3, 4 | 3eqtr4g 2247 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 df-in 3150 df-opab 4080 df-xp 4650 df-res 4656 |
This theorem is referenced by: reseq2i 4922 reseq2d 4925 resabs1 4954 resima2 4959 imaeq2 4984 resdisj 5075 relcoi1 5178 fressnfv 5724 tfrlem1 6334 tfrlem9 6345 tfr0dm 6348 tfrlemisucaccv 6351 tfrlemiubacc 6356 tfr1onlemsucaccv 6367 tfr1onlemubacc 6372 tfr1onlemaccex 6374 tfrcllemsucaccv 6380 tfrcllembxssdm 6382 tfrcllemubacc 6385 tfrcllemaccex 6387 tfrcllemres 6388 tfrcldm 6389 fnfi 6967 lmbr2 14191 lmff 14226 |
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