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Mirrors > Home > ILE Home > Th. List > imass2 | Unicode version |
Description: Subset theorem for image. Exercise 22(a) of [Enderton] p. 53. (Contributed by NM, 22-Mar-1998.) |
Ref | Expression |
---|---|
imass2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssres2 4841 | . . 3 | |
2 | rnss 4764 | . . 3 | |
3 | 1, 2 | syl 14 | . 2 |
4 | df-ima 4547 | . 2 | |
5 | df-ima 4547 | . 2 | |
6 | 3, 4, 5 | 3sstr4g 3135 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wss 3066 crn 4535 cres 4536 cima 4537 |
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-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-sn 3528 df-pr 3529 df-op 3531 df-br 3925 df-opab 3985 df-xp 4540 df-cnv 4542 df-dm 4544 df-rn 4545 df-res 4546 df-ima 4547 |
This theorem is referenced by: funimass1 5195 funimass2 5196 fvimacnv 5528 f1imass 5668 ecinxp 6497 sbthlem1 6838 sbthlem2 6839 iscnp4 12376 cnptopco 12380 cnntri 12382 cnrest2 12394 cnptopresti 12396 cnptoprest 12397 metcnp3 12669 |
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