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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 12393 | . 2 Slot | |
2 | 1str.g | . . 3 | |
3 | basendxnn 12392 | . . . . 5 | |
4 | opexg 4200 | . . . . 5 | |
5 | 3, 4 | mpan 421 | . . . 4 |
6 | snexg 4157 | . . . 4 | |
7 | 5, 6 | syl 14 | . . 3 |
8 | 2, 7 | eqeltrid 2251 | . 2 |
9 | funsng 5228 | . . . 4 | |
10 | 3, 9 | mpan 421 | . . 3 |
11 | 2 | funeqi 5203 | . . 3 |
12 | 10, 11 | sylibr 133 | . 2 |
13 | snidg 3599 | . . . 4 | |
14 | 5, 13 | syl 14 | . . 3 |
15 | 14, 2 | eleqtrrdi 2258 | . 2 |
16 | 1, 8, 12, 15 | strslfvd 12378 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1342 wcel 2135 cvv 2721 csn 3570 cop 3573 wfun 5176 cfv 5182 cn 8848 cnx 12334 cbs 12337 |
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 ax-cnex 7835 ax-resscn 7836 ax-1re 7838 ax-addrcl 7841 |
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-int 3819 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-res 4610 df-iota 5147 df-fun 5184 df-fv 5190 df-inn 8849 df-ndx 12340 df-slot 12341 df-base 12343 |
This theorem is referenced by: (None) |
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