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Mirrors > Home > ILE Home > Th. List > baseslid | GIF version |
Description: The base set extractor is a slot. (Contributed by Jim Kingdon, 31-Jan-2023.) |
Ref | Expression |
---|---|
baseslid | ⊢ (Base = Slot (Base‘ndx) ∧ (Base‘ndx) ∈ ℕ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | baseid 12285 | . 2 ⊢ Base = Slot (Base‘ndx) | |
2 | basendxnn 12287 | . 2 ⊢ (Base‘ndx) ∈ ℕ | |
3 | 1, 2 | ndxslid 12257 | 1 ⊢ (Base = Slot (Base‘ndx) ∧ (Base‘ndx) ∈ ℕ) |
Colors of variables: wff set class |
Syntax hints: ∧ wa 103 = wceq 1335 ∈ wcel 2128 ‘cfv 5171 ℕcn 8834 ndxcnx 12229 Slot cslot 12231 Basecbs 12232 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-13 2130 ax-14 2131 ax-ext 2139 ax-sep 4083 ax-pow 4136 ax-pr 4170 ax-un 4394 ax-cnex 7824 ax-resscn 7825 ax-1re 7827 ax-addrcl 7830 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-sbc 2938 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3774 df-int 3809 df-br 3967 df-opab 4027 df-mpt 4028 df-id 4254 df-xp 4593 df-rel 4594 df-cnv 4595 df-co 4596 df-dm 4597 df-rn 4598 df-res 4599 df-iota 5136 df-fun 5173 df-fv 5179 df-inn 8835 df-ndx 12235 df-slot 12236 df-base 12238 |
This theorem is referenced by: basfn 12289 opelstrbas 12329 1strbas 12331 2strbasg 12333 topnfn 12398 topnvalg 12405 topnidg 12406 setsmsbasg 12921 |
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