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Mirrors > Home > ILE Home > Th. List > rnss | Unicode version |
Description: Subset theorem for range. (Contributed by NM, 22-Mar-1998.) |
Ref | Expression |
---|---|
rnss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnvss 4759 | . . 3 | |
2 | dmss 4785 | . . 3 | |
3 | 1, 2 | syl 14 | . 2 |
4 | df-rn 4597 | . 2 | |
5 | df-rn 4597 | . 2 | |
6 | 3, 4, 5 | 3sstr4g 3171 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wss 3102 ccnv 4585 cdm 4586 crn 4587 |
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-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-sn 3566 df-pr 3567 df-op 3569 df-br 3966 df-opab 4026 df-cnv 4594 df-dm 4596 df-rn 4597 |
This theorem is referenced by: imass1 4961 imass2 4962 rnxpss2 5019 ssxpbm 5021 ssxp2 5023 ssrnres 5028 funssxp 5339 fssres 5345 dff2 5611 fliftf 5749 1stcof 6111 2ndcof 6112 smores 6239 tfrcllembfn 6304 caserel 7031 frecuzrdgtcl 10311 lmss 12657 txss12 12677 txbasval 12678 |
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