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Mirrors > Home > MPE Home > Th. List > dmresi | Structured version Visualization version Unicode version |
Description: The domain of a restricted identity function. (Contributed by NM, 27-Aug-2004.) |
Ref | Expression |
---|---|
dmresi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssv 3625 | . . 3 | |
2 | dmi 5340 | . . 3 | |
3 | 1, 2 | sseqtr4i 3638 | . 2 |
4 | ssdmres 5420 | . 2 | |
5 | 3, 4 | mpbi 220 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 cvv 3200 wss 3574 cid 5023 cdm 5114 cres 5116 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-id 5024 df-xp 5120 df-rel 5121 df-dm 5124 df-res 5126 |
This theorem is referenced by: fnresi 6008 idssxp 6009 iordsmo 7454 residfi 8247 hartogslem1 8447 dfac9 8958 hsmexlem5 9252 relexpdmg 13782 relexpfld 13789 relexpaddg 13793 dirdm 17234 islinds2 20152 lindsind2 20158 f1linds 20164 wilthlem3 24796 ausgrusgrb 26060 umgrres1 26206 usgrres1 26207 usgrexilem 26336 filnetlem3 32375 filnetlem4 32376 rclexi 37922 rtrclex 37924 rtrclexi 37928 cnvrcl0 37932 dfrtrcl5 37936 dfrcl2 37966 brfvrcld2 37984 iunrelexp0 37994 relexpiidm 37996 relexp01min 38005 idhe 38081 uspgrsprfo 41756 |
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