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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 4356 | . 2 | |
2 | uniexg 4356 | . 2 | |
3 | ssun2 3235 | . . . 4 | |
4 | dmrnssfld 4797 | . . . 4 | |
5 | 3, 4 | sstri 3101 | . . 3 |
6 | ssexg 4062 | . . 3 | |
7 | 5, 6 | mpan 420 | . 2 |
8 | 1, 2, 7 | 3syl 17 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1480 cvv 2681 cun 3064 wss 3066 cuni 3731 cdm 4534 crn 4535 |
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-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 ax-un 4350 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-rex 2420 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-opab 3985 df-cnv 4542 df-dm 4544 df-rn 4545 |
This theorem is referenced by: rnex 4801 imaexg 4888 xpexr2m 4975 elxp4 5021 elxp5 5022 cnvexg 5071 coexg 5078 fvexg 5433 cofunexg 6002 funrnex 6005 abrexexg 6009 2ndvalg 6034 tposexg 6148 iunon 6174 fopwdom 6723 djuexb 6922 focdmex 10526 shftfvalg 10583 ovshftex 10584 restval 12115 txvalex 12412 txval 12413 blbas 12591 xmettxlem 12667 xmettx 12668 |
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