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Mirrors > Home > ILE Home > Th. List > setsvalg | Unicode version |
Description: Value of the structure replacement function. (Contributed by Mario Carneiro, 30-Apr-2015.) |
Ref | Expression |
---|---|
setsvalg | sSet |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2692 | . 2 | |
2 | elex 2692 | . 2 | |
3 | resexg 4854 | . . . 4 | |
4 | snexg 4103 | . . . 4 | |
5 | unexg 4359 | . . . 4 | |
6 | 3, 4, 5 | syl2an 287 | . . 3 |
7 | simpl 108 | . . . . . 6 | |
8 | simpr 109 | . . . . . . . . 9 | |
9 | 8 | sneqd 3535 | . . . . . . . 8 |
10 | 9 | dmeqd 4736 | . . . . . . 7 |
11 | 10 | difeq2d 3189 | . . . . . 6 |
12 | 7, 11 | reseq12d 4815 | . . . . 5 |
13 | 12, 9 | uneq12d 3226 | . . . 4 |
14 | df-sets 11955 | . . . 4 sSet | |
15 | 13, 14 | ovmpoga 5893 | . . 3 sSet |
16 | 6, 15 | mpd3an3 1316 | . 2 sSet |
17 | 1, 2, 16 | syl2an 287 | 1 sSet |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1331 wcel 1480 cvv 2681 cdif 3063 cun 3064 csn 3522 cdm 4534 cres 4536 (class class class)co 5767 sSet csts 11946 |
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 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 ax-un 4350 ax-setind 4447 |
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 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ne 2307 df-ral 2419 df-rex 2420 df-rab 2423 df-v 2683 df-sbc 2905 df-dif 3068 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-id 4210 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-res 4546 df-iota 5083 df-fun 5120 df-fv 5126 df-ov 5770 df-oprab 5771 df-mpo 5772 df-sets 11955 |
This theorem is referenced by: setsvala 11979 setsfun 11983 setsfun0 11984 setsresg 11986 |
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