Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > eldm2 | Structured version Visualization version 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 5320 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wex 1704 wcel 1990 cvv 3200 cop 4183 cdm 5114 |
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 |
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-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 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-dm 5124 |
This theorem is referenced by: dmss 5323 opeldm 5328 dmin 5332 dmiun 5333 dmuni 5334 dm0 5339 reldm0 5343 dmrnssfld 5384 dmcoss 5385 dmcosseq 5387 dmres 5419 iss 5447 dmsnopg 5606 relssdmrn 5656 funssres 5930 dmfco 6272 fun11iun 7126 wfrlem12 7426 axdc3lem2 9273 gsum2d2 18373 cnlnssadj 28939 prsdm 29960 eldm3 31651 dfdm5 31676 frrlem11 31792 iss2 34112 |
Copyright terms: Public domain | W3C validator |