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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 4976 |
. 2
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2 | dfdm4 4814 |
. 2
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3 | 1, 2 | sseqtrri 3190 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4205 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-br 4001 df-opab 4062 df-xp 4628 df-cnv 4630 df-dm 4632 df-rn 4633 df-res 4634 df-ima 4635 |
This theorem is referenced by: fvimacnvi 5625 elpreima 5630 fconst4m 5731 nn0supp 9204 fisumss 11371 fprodssdc 11569 1arith 12335 cnpnei 13352 cnclima 13356 cnntri 13357 cnntr 13358 cncnp 13363 cnrest2 13369 cndis 13374 txcnmpt 13406 txdis1cn 13411 hmeoimaf1o 13447 xmeter 13569 |
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