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Mirrors > Home > ILE Home > Th. List > fex2 | Unicode version |
Description: A function with bounded domain and range is a set. This version is proven without the Axiom of Replacement. (Contributed by Mario Carneiro, 24-Jun-2015.) |
Ref | Expression |
---|---|
fex2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xpexg 4623 | . . 3 | |
2 | 1 | 3adant1 984 | . 2 |
3 | fssxp 5260 | . . 3 | |
4 | 3 | 3ad2ant1 987 | . 2 |
5 | 2, 4 | ssexd 4038 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 w3a 947 wcel 1465 cvv 2660 wss 3041 cxp 4507 wf 5089 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 ax-un 4325 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-xp 4515 df-rel 4516 df-cnv 4517 df-dm 4519 df-rn 4520 df-fun 5095 df-fn 5096 df-f 5097 |
This theorem is referenced by: elmapg 6523 f1oen2g 6617 f1dom2g 6618 dom3d 6636 mapxpen 6710 climrecvg1n 11085 cnpfval 12291 txcn 12371 blfvalps 12481 |
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