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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 4739 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1331 cdm 4539 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-sn 3533 df-pr 3534 df-op 3536 df-br 3930 df-dm 4549 |
This theorem is referenced by: dmxpm 4759 dmxpid 4760 dmxpin 4761 rncoss 4809 rncoeq 4812 rnun 4947 rnin 4948 rnxpm 4968 rnxpss 4970 imainrect 4984 dmpropg 5011 dmtpop 5014 rnsnopg 5017 fntpg 5179 fnreseql 5530 dmoprab 5852 reldmmpo 5882 elmpocl 5968 tfrlem8 6215 tfr2a 6218 tfrlemi14d 6230 tfr1onlemres 6246 tfri1dALT 6248 tfrcllemres 6259 xpassen 6724 sbthlemi5 6849 casedm 6971 djudm 6990 ctssdccl 6996 dmaddpi 7133 dmmulpi 7134 dmaddpq 7187 dmmulpq 7188 axaddf 7676 axmulf 7677 ennnfonelemom 11921 ennnfonelemdm 11933 |
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