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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 4535 | . 2 | |
3 | 1, 2 | ax-mp 7 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1243 cdm 4345 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-sn 3381 df-pr 3382 df-op 3384 df-br 3765 df-dm 4355 |
This theorem is referenced by: dmxpm 4555 dmxpinm 4556 rncoss 4602 rncoeq 4605 rnun 4732 rnin 4733 rnxpm 4752 rnxpss 4754 imainrect 4766 dmpropg 4793 dmtpop 4796 rnsnopg 4799 fntpg 4955 fnreseql 5277 dmoprab 5585 reldmmpt2 5612 elmpt2cl 5698 tfrlem8 5934 tfr2a 5936 tfrlemi14d 5947 xpassen 6304 dmaddpi 6423 dmmulpi 6424 dmaddpq 6477 dmmulpq 6478 |
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