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Mirrors > Home > ILE Home > Th. List > resdmdfsn | Unicode version |
Description: Restricting a relation to its domain without a set is the same as restricting the relation to the universe without this set. (Contributed by AV, 2-Dec-2018.) |
Ref | Expression |
---|---|
resdmdfsn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | indif1 3260 |
. . . 4
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2 | incom 3207 |
. . . . . 6
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3 | inv1 3338 |
. . . . . 6
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4 | 2, 3 | eqtri 2115 |
. . . . 5
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5 | 4 | difeq1i 3129 |
. . . 4
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6 | 1, 5 | eqtri 2115 |
. . 3
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7 | 6 | reseq2i 4742 |
. 2
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8 | resindm 4787 |
. 2
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9 | 7, 8 | syl5reqr 2142 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 582 ax-in2 583 ax-io 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-14 1457 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 ax-sep 3978 ax-pow 4030 ax-pr 4060 |
This theorem depends on definitions: df-bi 116 df-3an 929 df-tru 1299 df-nf 1402 df-sb 1700 df-clab 2082 df-cleq 2088 df-clel 2091 df-nfc 2224 df-ral 2375 df-rex 2376 df-rab 2379 df-v 2635 df-dif 3015 df-un 3017 df-in 3019 df-ss 3026 df-pw 3451 df-sn 3472 df-pr 3473 df-op 3475 df-br 3868 df-opab 3922 df-xp 4473 df-rel 4474 df-dm 4477 df-res 4479 |
This theorem is referenced by: funresdfunsnss 5539 funresdfunsndc 6305 |
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