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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imassrn 4999 |
. 2
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2 | dfdm4 4837 |
. 2
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3 | 1, 2 | sseqtrri 3205 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4192 ax-pr 4227 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-br 4019 df-opab 4080 df-xp 4650 df-cnv 4652 df-dm 4654 df-rn 4655 df-res 4656 df-ima 4657 |
This theorem is referenced by: fvimacnvi 5651 elpreima 5656 fconst4m 5757 pw2f1odclem 6862 nn0supp 9258 fisumss 11432 fprodssdc 11630 1arith 12399 ghmpreima 13205 cnpnei 14179 cnclima 14183 cnntri 14184 cnntr 14185 cncnp 14190 cnrest2 14196 cndis 14201 txcnmpt 14233 txdis1cn 14238 hmeoimaf1o 14274 xmeter 14396 |
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