Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 4708 | . . 3 | |
2 | dmss 4708 | . . 3 | |
3 | 1, 2 | anim12i 336 | . 2 |
4 | eqss 3082 | . 2 | |
5 | eqss 3082 | . 2 | |
6 | 3, 4, 5 | 3imtr4i 200 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1316 wss 3041 cdm 4509 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 df-dm 4519 |
This theorem is referenced by: dmeqi 4710 dmeqd 4711 xpid11 4732 sqxpeq0 4932 fneq1 5181 eqfnfv2 5487 offval 5957 ofrfval 5958 offval3 6000 smoeq 6155 tfrlemi14d 6198 tfr1onlemres 6214 tfrcllemres 6227 rdgivallem 6246 rdgon 6251 rdg0 6252 frec0g 6262 freccllem 6267 frecfcllem 6269 frecsuclem 6271 frecsuc 6272 ereq1 6404 fundmeng 6669 acfun 7031 ccfunen 7047 ennnfonelemj0 11841 ennnfonelemg 11843 ennnfonelemp1 11846 ennnfonelemom 11848 ennnfonelemnn0 11862 blfvalps 12481 reldvg 12744 |
Copyright terms: Public domain | W3C validator |