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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 4400 | . 2 | |
2 | uniexg 4400 | . 2 | |
3 | ssun2 3271 | . . . 4 | |
4 | dmrnssfld 4850 | . . . 4 | |
5 | 3, 4 | sstri 3137 | . . 3 |
6 | ssexg 4104 | . . 3 | |
7 | 5, 6 | mpan 421 | . 2 |
8 | 1, 2, 7 | 3syl 17 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 2128 cvv 2712 cun 3100 wss 3102 cuni 3773 cdm 4587 crn 4588 |
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-13 2130 ax-14 2131 ax-ext 2139 ax-sep 4083 ax-pow 4136 ax-pr 4170 ax-un 4394 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3774 df-br 3967 df-opab 4027 df-cnv 4595 df-dm 4597 df-rn 4598 |
This theorem is referenced by: rnex 4854 imaexg 4941 xpexr2m 5028 elxp4 5074 elxp5 5075 cnvexg 5124 coexg 5131 fvexg 5488 cofunexg 6060 funrnex 6063 abrexexg 6067 2ndvalg 6092 tposexg 6206 iunon 6232 fopwdom 6782 djuexb 6989 focdmex 10665 shftfvalg 10722 ovshftex 10723 restval 12399 txvalex 12696 txval 12697 blbas 12875 xmettxlem 12951 xmettx 12952 |
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