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Mirrors > Home > ILE Home > Th. List > imassrn | Unicode version |
Description: The image of a class is a subset of its range. Theorem 3.16(xi) of [Monk1] p. 39. (Contributed by NM, 31-Mar-1995.) |
Ref | Expression |
---|---|
imassrn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exsimpr 1598 | . . 3 | |
2 | 1 | ss2abi 3200 | . 2 |
3 | dfima3 4931 | . 2 | |
4 | dfrn3 4775 | . 2 | |
5 | 2, 3, 4 | 3sstr4i 3169 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wex 1472 wcel 2128 cab 2143 wss 3102 cop 3563 crn 4587 cima 4589 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-br 3966 df-opab 4026 df-xp 4592 df-cnv 4594 df-dm 4596 df-rn 4597 df-res 4598 df-ima 4599 |
This theorem is referenced by: imaexg 4940 0ima 4946 cnvimass 4949 fimacnv 5596 f1opw2 6026 smores2 6241 ecss 6521 f1imaen2g 6738 fopwdom 6781 ssenen 6796 phplem4dom 6807 isinfinf 6842 fiintim 6873 sbthlem2 6902 sbthlemi3 6903 sbthlemi5 6905 sbthlemi6 6906 ctssdccl 7055 ctinf 12170 ssnnctlemct 12186 cnptoprest2 12651 hmeontr 12724 hmeores 12726 tgqioo 12958 |
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