Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > basfn | Structured version Visualization version 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 | df-base 16472 | . 2 ⊢ Base = Slot 1 | |
2 | 1 | slotfn 16484 | 1 ⊢ Base Fn V |
Colors of variables: wff setvar class |
Syntax hints: Vcvv 3486 Fn wfn 6336 1c1 10524 Basecbs 16466 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2793 ax-sep 5189 ax-nul 5196 ax-pr 5316 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-mo 2622 df-eu 2654 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-ral 3143 df-rex 3144 df-rab 3147 df-v 3488 df-sbc 3764 df-dif 3927 df-un 3929 df-in 3931 df-ss 3940 df-nul 4280 df-if 4454 df-sn 4554 df-pr 4556 df-op 4560 df-uni 4825 df-br 5053 df-opab 5115 df-mpt 5133 df-id 5446 df-xp 5547 df-rel 5548 df-cnv 5549 df-co 5550 df-dm 5551 df-iota 6300 df-fun 6343 df-fn 6344 df-fv 6349 df-slot 16470 df-base 16472 |
This theorem is referenced by: bascnvimaeqv 17354 isnumbasgrplem1 39793 isnumbasgrplem2 39796 dfacbasgrp 39800 |
Copyright terms: Public domain | W3C validator |