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Mirrors > Home > ILE Home > Th. List > dmeq | Unicode version |
Description: Equality theorem for domain. (Contributed by NM, 11-Aug-1994.) |
Ref | Expression |
---|---|
dmeq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dmss 4785 | . . 3 | |
2 | dmss 4785 | . . 3 | |
3 | 1, 2 | anim12i 336 | . 2 |
4 | eqss 3143 | . 2 | |
5 | eqss 3143 | . 2 | |
6 | 3, 4, 5 | 3imtr4i 200 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1335 wss 3102 cdm 4586 |
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 4596 |
This theorem is referenced by: dmeqi 4787 dmeqd 4788 xpid11 4809 sqxpeq0 5009 fneq1 5258 eqfnfv2 5566 offval 6039 ofrfval 6040 offval3 6082 smoeq 6237 tfrlemi14d 6280 tfr1onlemres 6296 tfrcllemres 6309 rdgivallem 6328 rdgon 6333 rdg0 6334 frec0g 6344 freccllem 6349 frecfcllem 6351 frecsuclem 6353 frecsuc 6354 ereq1 6487 fundmeng 6752 acfun 7142 ccfunen 7184 ennnfonelemj0 12141 ennnfonelemg 12143 ennnfonelemp1 12146 ennnfonelemom 12148 ennnfonelemnn0 12162 blfvalps 12796 reldvg 13059 |
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