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Mirrors > Home > ILE Home > Th. List > strfvssn | Unicode version |
Description: A structure component extractor produces a value which is contained in a set dependent on , but not . This is sometimes useful for showing sethood. (Contributed by Mario Carneiro, 15-Aug-2015.) (Revised by Jim Kingdon, 19-Jan-2023.) |
Ref | Expression |
---|---|
strfvssn.c | Slot |
strfvssn.s | |
strfvssn.n |
Ref | Expression |
---|---|
strfvssn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | strfvssn.c | . . 3 Slot | |
2 | strfvssn.s | . . 3 | |
3 | strfvssn.n | . . 3 | |
4 | 1, 2, 3 | strnfvnd 12351 | . 2 |
5 | 3 | elexd 2734 | . . 3 |
6 | fvssunirng 5495 | . . 3 | |
7 | 5, 6 | syl 14 | . 2 |
8 | 4, 7 | eqsstrd 3173 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1342 wcel 2135 cvv 2721 wss 3111 cuni 3783 crn 4599 cfv 5182 cn 8848 Slot cslot 12330 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-13 2137 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 ax-un 4405 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-sbc 2947 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-opab 4038 df-mpt 4039 df-id 4265 df-xp 4604 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-rn 4609 df-iota 5147 df-fun 5184 df-fv 5190 df-slot 12335 |
This theorem is referenced by: (None) |
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