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Mirrors > Home > ILE Home > Th. List > mapvalg | Unicode version |
Description: The value of set exponentiation. is the set of all functions that map from to . Definition 10.24 of [Kunen] p. 24. (Contributed by NM, 8-Dec-2003.) (Revised by Mario Carneiro, 8-Sep-2013.) |
Ref | Expression |
---|---|
mapvalg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mapex 6548 | . . 3 | |
2 | 1 | ancoms 266 | . 2 |
3 | elex 2697 | . . 3 | |
4 | elex 2697 | . . 3 | |
5 | feq3 5257 | . . . . . 6 | |
6 | 5 | abbidv 2257 | . . . . 5 |
7 | feq2 5256 | . . . . . 6 | |
8 | 7 | abbidv 2257 | . . . . 5 |
9 | df-map 6544 | . . . . 5 | |
10 | 6, 8, 9 | ovmpog 5905 | . . . 4 |
11 | 10 | 3expia 1183 | . . 3 |
12 | 3, 4, 11 | syl2an 287 | . 2 |
13 | 2, 12 | mpd 13 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1331 wcel 1480 cab 2125 cvv 2686 wf 5119 (class class class)co 5774 cmap 6542 |
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-in1 603 ax-in2 604 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 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 ax-un 4355 ax-setind 4452 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ne 2309 df-ral 2421 df-rex 2422 df-v 2688 df-sbc 2910 df-dif 3073 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-rn 4550 df-iota 5088 df-fun 5125 df-fn 5126 df-f 5127 df-fv 5131 df-ov 5777 df-oprab 5778 df-mpo 5779 df-map 6544 |
This theorem is referenced by: mapval 6554 elmapg 6555 ixpconstg 6601 cnovex 12365 ispsmet 12492 cncfval 12728 |
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