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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 1611 | . . 3 | |
2 | 1 | ss2abi 3219 | . 2 |
3 | dfima3 4956 | . 2 | |
4 | dfrn3 4800 | . 2 | |
5 | 2, 3, 4 | 3sstr4i 3188 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wex 1485 wcel 2141 cab 2156 wss 3121 cop 3586 crn 4612 cima 4614 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-br 3990 df-opab 4051 df-xp 4617 df-cnv 4619 df-dm 4621 df-rn 4622 df-res 4623 df-ima 4624 |
This theorem is referenced by: imaexg 4965 0ima 4971 cnvimass 4974 fimacnv 5625 f1opw2 6055 smores2 6273 ecss 6554 f1imaen2g 6771 fopwdom 6814 ssenen 6829 phplem4dom 6840 isinfinf 6875 fiintim 6906 sbthlem2 6935 sbthlemi3 6936 sbthlemi5 6938 sbthlemi6 6939 ctssdccl 7088 ctinf 12385 ssnnctlemct 12401 mhmima 12706 cnptoprest2 13034 hmeontr 13107 hmeores 13109 tgqioo 13341 |
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