Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 4784 | . . 3 | |
2 | dmss 4810 | . . 3 | |
3 | 1, 2 | syl 14 | . 2 |
4 | df-rn 4622 | . 2 | |
5 | df-rn 4622 | . 2 | |
6 | 3, 4, 5 | 3sstr4g 3190 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wss 3121 ccnv 4610 cdm 4611 crn 4612 |
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-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-sn 3589 df-pr 3590 df-op 3592 df-br 3990 df-opab 4051 df-cnv 4619 df-dm 4621 df-rn 4622 |
This theorem is referenced by: imass1 4986 imass2 4987 rnxpss2 5044 ssxpbm 5046 ssxp2 5048 ssrnres 5053 funssxp 5367 fssres 5373 dff2 5640 fliftf 5778 1stcof 6142 2ndcof 6143 smores 6271 tfrcllembfn 6336 caserel 7064 frecuzrdgtcl 10368 lmss 13040 txss12 13060 txbasval 13061 |
Copyright terms: Public domain | W3C validator |