![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > basfn | GIF version |
Description: The base set extractor is a function on V. (Contributed by Stefan O'Rear, 8-Jul-2015.) |
Ref | Expression |
---|---|
basfn | ⊢ Base Fn V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | baseslid 12488 | . 2 ⊢ (Base = Slot (Base‘ndx) ∧ (Base‘ndx) ∈ ℕ) | |
2 | 1 | slotslfn 12458 | 1 ⊢ Base Fn V |
Colors of variables: wff set class |
Syntax hints: Vcvv 2737 Fn wfn 5206 Basecbs 12432 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4205 ax-un 4429 ax-cnex 7880 ax-resscn 7881 ax-1re 7883 ax-addrcl 7886 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-sbc 2963 df-un 3133 df-in 3135 df-ss 3142 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-int 3843 df-br 4001 df-opab 4062 df-mpt 4063 df-id 4289 df-xp 4628 df-rel 4629 df-cnv 4630 df-co 4631 df-dm 4632 df-rn 4633 df-res 4634 df-iota 5173 df-fun 5213 df-fn 5214 df-fv 5219 df-inn 8896 df-ndx 12435 df-slot 12436 df-base 12438 |
This theorem is referenced by: basmex 12490 basmexd 12491 ressbas2d 12497 strressid 12499 ressval3d 12500 ismgm 12655 ismgmn0 12656 plusffvalg 12660 grpidvalg 12671 fn0g 12673 issgrp 12688 ismnddef 12698 issubmnd 12722 ismhm 12730 issubm 12740 grppropstrg 12772 grpinvfvalg 12792 grpinvval 12793 grpinvfng 12794 grpsubfvalg 12795 grpsubval 12796 grplactfval 12847 mulgfvalg 12861 mulgval 12862 mulgfng 12863 issrg 12961 isring 12996 ringidss 13025 reldvdsrsrg 13073 dvdsrvald 13074 dvdsrex 13079 unitgrp 13097 unitabl 13098 invrfvald 13103 unitlinv 13107 unitrinv 13108 |
Copyright terms: Public domain | W3C validator |