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Mirrors > Home > ILE Home > Th. List > cnvimass | Unicode version |
Description: A preimage under any class is included in the domain of the class. (Contributed by FL, 29-Jan-2007.) |
Ref | Expression |
---|---|
cnvimass |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imassrn 4862 | . 2 | |
2 | dfdm4 4701 | . 2 | |
3 | 1, 2 | sseqtrri 3102 | 1 |
Colors of variables: wff set class |
Syntax hints: wss 3041 ccnv 4508 cdm 4509 crn 4510 cima 4512 |
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-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 df-opab 3960 df-xp 4515 df-cnv 4517 df-dm 4519 df-rn 4520 df-res 4521 df-ima 4522 |
This theorem is referenced by: fvimacnvi 5502 elpreima 5507 fconst4m 5608 nn0supp 8997 fisumss 11129 cnpnei 12315 cnclima 12319 cnntri 12320 cnntr 12321 cncnp 12326 cnrest2 12332 cndis 12337 txcnmpt 12369 txdis1cn 12374 hmeoimaf1o 12410 xmeter 12532 |
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