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Mirrors > Home > MPE Home > Th. List > filsspw | Structured version Visualization version Unicode version |
Description: A filter is a subset of the power set of the base set. (Contributed by Stefan O'Rear, 28-Jul-2015.) |
Ref | Expression |
---|---|
filsspw |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | filfbas 21652 | . 2 | |
2 | fbsspw 21636 | . 2 | |
3 | 1, 2 | syl 17 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1990 wss 3574 cpw 4158 cfv 5888 cfbas 19734 cfil 21649 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-nel 2898 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fv 5896 df-fbas 19743 df-fil 21650 |
This theorem is referenced by: isfil2 21660 infil 21667 filunibas 21685 trfg 21695 isufil2 21712 filssufilg 21715 ssufl 21722 ufileu 21723 filufint 21724 uffixfr 21727 elflim 21775 fclsfnflim 21831 flimfnfcls 21832 metust 22363 cfilresi 23093 cmetss 23113 |
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