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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 4892 | . 2 | |
2 | dfdm4 4731 | . 2 | |
3 | 1, 2 | sseqtrri 3132 | 1 |
Colors of variables: wff set class |
Syntax hints: wss 3071 ccnv 4538 cdm 4539 crn 4540 cima 4542 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-br 3930 df-opab 3990 df-xp 4545 df-cnv 4547 df-dm 4549 df-rn 4550 df-res 4551 df-ima 4552 |
This theorem is referenced by: fvimacnvi 5534 elpreima 5539 fconst4m 5640 nn0supp 9029 fisumss 11161 cnpnei 12388 cnclima 12392 cnntri 12393 cnntr 12394 cncnp 12399 cnrest2 12405 cndis 12410 txcnmpt 12442 txdis1cn 12447 hmeoimaf1o 12483 xmeter 12605 |
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