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Mirrors > Home > ILE Home > Th. List > rnexg | Unicode version |
Description: The range of a set is a set. Corollary 6.8(3) of [TakeutiZaring] p. 26. Similar to Lemma 3D of [Enderton] p. 41. (Contributed by NM, 31-Mar-1995.) |
Ref | Expression |
---|---|
rnexg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uniexg 4424 | . 2 | |
2 | uniexg 4424 | . 2 | |
3 | ssun2 3291 | . . . 4 | |
4 | dmrnssfld 4874 | . . . 4 | |
5 | 3, 4 | sstri 3156 | . . 3 |
6 | ssexg 4128 | . . 3 | |
7 | 5, 6 | mpan 422 | . 2 |
8 | 1, 2, 7 | 3syl 17 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 2141 cvv 2730 cun 3119 wss 3121 cuni 3796 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-13 2143 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 ax-un 4418 |
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-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-uni 3797 df-br 3990 df-opab 4051 df-cnv 4619 df-dm 4621 df-rn 4622 |
This theorem is referenced by: rnex 4878 imaexg 4965 xpexr2m 5052 elxp4 5098 elxp5 5099 cnvexg 5148 coexg 5155 fvexg 5515 cofunexg 6088 funrnex 6093 abrexexg 6097 2ndvalg 6122 tposexg 6237 iunon 6263 fopwdom 6814 djuexb 7021 focdmex 10721 shftfvalg 10782 ovshftex 10783 restval 12585 txvalex 13048 txval 13049 blbas 13227 xmettxlem 13303 xmettx 13304 |
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