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Mirrors > Home > ILE Home > Th. List > strslfv2d | Unicode version |
Description: Deduction version of strslfv 11930. (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 11906 | . 2 |
7 | cnvcnv2 4962 | . . . 4 | |
8 | 7 | fveq1i 5390 | . . 3 |
9 | 5 | elexd 2673 | . . . 4 |
10 | fvres 5413 | . . . 4 | |
11 | 9, 10 | syl 14 | . . 3 |
12 | 8, 11 | syl5eq 2162 | . 2 |
13 | strfv2d.f | . . 3 | |
14 | strfv2d.n | . . . . 5 | |
15 | strfv2d.c | . . . . . . 7 | |
16 | 15 | elexd 2673 | . . . . . 6 |
17 | 9, 16 | opelxpd 4542 | . . . . 5 |
18 | 14, 17 | elind 3231 | . . . 4 |
19 | cnvcnv 4961 | . . . 4 | |
20 | 18, 19 | eleqtrrdi 2211 | . . 3 |
21 | funopfv 5429 | . . 3 | |
22 | 13, 20, 21 | sylc 62 | . 2 |
23 | 6, 12, 22 | 3eqtr2rd 2157 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1316 wcel 1465 cvv 2660 cin 3040 cop 3500 cxp 4507 ccnv 4508 cres 4511 wfun 5087 cfv 5093 cn 8688 cnx 11883 Slot cslot 11885 |
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-sbc 2883 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-mpt 3961 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-rn 4520 df-res 4521 df-iota 5058 df-fun 5095 df-fv 5101 df-slot 11890 |
This theorem is referenced by: strslfv2 11929 strslfv 11930 opelstrsl 11982 |
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