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Mirrors > Home > MPE Home > Th. List > resres | Structured version Visualization version Unicode version |
Description: The restriction of a restriction. (Contributed by NM, 27-Mar-2008.) |
Ref | Expression |
---|---|
resres |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-res 4851 |
. 2
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2 | df-res 4851 |
. . 3
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3 | 2 | ineq1i 3621 |
. 2
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4 | xpindir 4974 |
. . . 4
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5 | 4 | ineq2i 3622 |
. . 3
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6 | df-res 4851 |
. . 3
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7 | inass 3633 |
. . 3
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8 | 5, 6, 7 | 3eqtr4ri 2504 |
. 2
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9 | 1, 3, 8 | 3eqtri 2497 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-9 1913 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 ax-sep 4518 ax-nul 4527 ax-pr 4639 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-3an 1009 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-clab 2458 df-cleq 2464 df-clel 2467 df-nfc 2601 df-ne 2643 df-ral 2761 df-rex 2762 df-rab 2765 df-v 3033 df-dif 3393 df-un 3395 df-in 3397 df-ss 3404 df-nul 3723 df-if 3873 df-sn 3960 df-pr 3962 df-op 3966 df-opab 4455 df-xp 4845 df-rel 4846 df-res 4851 |
This theorem is referenced by: rescom 5135 resabs1 5139 resima2 5144 resmpt3 5161 resdisj 5272 rescnvcnv 5305 fresin 5764 resdif 5848 curry1 6907 curry2 6910 wfrlem4 7057 pmresg 7517 gruima 9245 rlimres 13699 lo1res 13700 rlimresb 13706 lo1eq 13709 rlimeq 13710 fsets 15227 setsid 15242 sscres 15806 gsumzres 17621 txkgen 20744 tsmsres 21236 ressxms 21618 ressms 21619 dvres 22945 dvres3a 22948 cpnres 22970 dvmptres3 22989 rlimcnp2 23971 df1stres 28359 df2ndres 28360 indf1ofs 28921 frrlem4 30588 dfrcl2 36337 relexpaddss 36381 fouriersw 38207 fouriercn 38208 |
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