Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > 1strbas | Unicode version |
Description: The base set of a constructed one-slot structure. (Contributed by AV, 27-Mar-2020.) |
Ref | Expression |
---|---|
1str.g |
Ref | Expression |
---|---|
1strbas |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | baseslid 11942 | . 2 Slot | |
2 | 1str.g | . . 3 | |
3 | basendxnn 11941 | . . . . 5 | |
4 | opexg 4120 | . . . . 5 | |
5 | 3, 4 | mpan 420 | . . . 4 |
6 | snexg 4078 | . . . 4 | |
7 | 5, 6 | syl 14 | . . 3 |
8 | 2, 7 | eqeltrid 2204 | . 2 |
9 | funsng 5139 | . . . 4 | |
10 | 3, 9 | mpan 420 | . . 3 |
11 | 2 | funeqi 5114 | . . 3 |
12 | 10, 11 | sylibr 133 | . 2 |
13 | snidg 3524 | . . . 4 | |
14 | 5, 13 | syl 14 | . . 3 |
15 | 14, 2 | eleqtrrdi 2211 | . 2 |
16 | 1, 8, 12, 15 | strslfvd 11927 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1316 wcel 1465 cvv 2660 csn 3497 cop 3500 wfun 5087 cfv 5093 cn 8688 cnx 11883 cbs 11886 |
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 ax-cnex 7679 ax-resscn 7680 ax-1re 7682 ax-addrcl 7685 |
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-int 3742 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-inn 8689 df-ndx 11889 df-slot 11890 df-base 11892 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |