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Mirrors > Home > ILE Home > Th. List > dmeqi | Unicode version |
Description: Equality inference for domain. (Contributed by NM, 4-Mar-2004.) |
Ref | Expression |
---|---|
dmeqi.1 |
Ref | Expression |
---|---|
dmeqi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dmeqi.1 | . 2 | |
2 | dmeq 4785 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1335 cdm 4585 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-sn 3566 df-pr 3567 df-op 3569 df-br 3966 df-dm 4595 |
This theorem is referenced by: dmxpm 4805 dmxpid 4806 dmxpin 4807 rncoss 4855 rncoeq 4858 rnun 4993 rnin 4994 rnxpm 5014 rnxpss 5016 imainrect 5030 dmpropg 5057 dmtpop 5060 rnsnopg 5063 fntpg 5225 fnreseql 5576 dmoprab 5899 reldmmpo 5929 elmpocl 6015 tfrlem8 6262 tfr2a 6265 tfrlemi14d 6277 tfr1onlemres 6293 tfri1dALT 6295 tfrcllemres 6306 xpassen 6772 sbthlemi5 6902 casedm 7025 djudm 7044 ctssdccl 7050 dmaddpi 7240 dmmulpi 7241 dmaddpq 7294 dmmulpq 7295 axaddf 7783 axmulf 7784 ennnfonelemom 12124 ennnfonelemdm 12136 |
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