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Mirrors > Home > ILE Home > Th. List > eldm2 | Unicode version |
Description: Membership in a domain. Theorem 4 of [Suppes] p. 59. (Contributed by NM, 1-Aug-1994.) |
Ref | Expression |
---|---|
eldm.1 |
Ref | Expression |
---|---|
eldm2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eldm.1 | . 2 | |
2 | eldm2g 4797 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wex 1479 wcel 2135 cvv 2724 cop 3576 cdm 4601 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2726 df-un 3118 df-sn 3579 df-pr 3580 df-op 3582 df-br 3980 df-dm 4611 |
This theorem is referenced by: dmss 4800 opeldm 4804 dmin 4809 dmiun 4810 dmuni 4811 dm0 4815 reldm0 4819 dmrnssfld 4864 dmcoss 4870 dmcosseq 4872 dmres 4902 iss 4927 dmxpss 5031 dmsnopg 5072 relssdmrn 5121 funssres 5227 fun11iun 5450 tfrlemibxssdm 6289 tfr1onlembxssdm 6305 tfrcllembxssdm 6318 |
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