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Mirrors > Home > ILE Home > Th. List > relres | Unicode version |
Description: A restriction is a relation. Exercise 12 of [TakeutiZaring] p. 25. (Contributed by NM, 2-Aug-1994.) (Proof shortened by Andrew Salmon, 27-Aug-2011.) |
Ref | Expression |
---|---|
relres |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-res 4638 |
. . 3
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2 | inss2 3356 |
. . 3
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3 | 1, 2 | eqsstri 3187 |
. 2
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4 | relxp 4735 |
. 2
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5 | relss 4713 |
. 2
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6 | 3, 4, 5 | mp2 16 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-in 3135 df-ss 3142 df-opab 4065 df-xp 4632 df-rel 4633 df-res 4638 |
This theorem is referenced by: elres 4943 resiexg 4952 iss 4953 dfres2 4959 restidsing 4963 issref 5011 asymref 5014 poirr2 5021 cnvcnvres 5092 resco 5133 ressn 5169 funssres 5258 fnresdisj 5326 fnres 5332 fcnvres 5399 nfunsn 5549 fsnunfv 5717 resfunexgALT 6108 setsresg 12494 |
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