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Mirrors > Home > ILE Home > Th. List > strslfv2d | Unicode version |
Description: Deduction version of strslfv 12042. (Contributed by Mario Carneiro, 30-Apr-2015.) (Revised by Jim Kingdon, 30-Jan-2023.) |
Ref | Expression |
---|---|
strslfv2d.e | Slot |
strfv2d.s | |
strfv2d.f | |
strfv2d.n | |
strfv2d.c |
Ref | Expression |
---|---|
strslfv2d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | strslfv2d.e | . . . 4 Slot | |
2 | 1 | simpli 110 | . . 3 Slot |
3 | strfv2d.s | . . 3 | |
4 | 1 | simpri 112 | . . . 4 |
5 | 4 | a1i 9 | . . 3 |
6 | 2, 3, 5 | strnfvnd 12018 | . 2 |
7 | cnvcnv2 5000 | . . . 4 | |
8 | 7 | fveq1i 5430 | . . 3 |
9 | 5 | elexd 2702 | . . . 4 |
10 | fvres 5453 | . . . 4 | |
11 | 9, 10 | syl 14 | . . 3 |
12 | 8, 11 | syl5eq 2185 | . 2 |
13 | strfv2d.f | . . 3 | |
14 | strfv2d.n | . . . . 5 | |
15 | strfv2d.c | . . . . . . 7 | |
16 | 15 | elexd 2702 | . . . . . 6 |
17 | 9, 16 | opelxpd 4580 | . . . . 5 |
18 | 14, 17 | elind 3266 | . . . 4 |
19 | cnvcnv 4999 | . . . 4 | |
20 | 18, 19 | eleqtrrdi 2234 | . . 3 |
21 | funopfv 5469 | . . 3 | |
22 | 13, 20, 21 | sylc 62 | . 2 |
23 | 6, 12, 22 | 3eqtr2rd 2180 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1332 wcel 1481 cvv 2689 cin 3075 cop 3535 cxp 4545 ccnv 4546 cres 4549 wfun 5125 cfv 5131 cn 8744 cnx 11995 Slot cslot 11997 |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 ax-un 4363 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-v 2691 df-sbc 2914 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-opab 3998 df-mpt 3999 df-id 4223 df-xp 4553 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-rn 4558 df-res 4559 df-iota 5096 df-fun 5133 df-fv 5139 df-slot 12002 |
This theorem is referenced by: strslfv2 12041 strslfv 12042 opelstrsl 12094 |
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