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Mirrors > Home > MPE Home > Th. List > ssfid | Structured version Visualization version Unicode version |
Description: A subset of a finite set is finite, deduction version of ssfi 8180. (Contributed by Glauco Siliprandi, 21-Nov-2020.) |
Ref | Expression |
---|---|
ssfid.1 | |
ssfid.2 |
Ref | Expression |
---|---|
ssfid |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssfid.1 | . 2 | |
2 | ssfid.2 | . 2 | |
3 | ssfi 8180 | . 2 | |
4 | 1, 2, 3 | syl2anc 693 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1990 wss 3574 cfn 7955 |
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 ax-un 6949 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3or 1038 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-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-pss 3590 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-tp 4182 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-tr 4753 df-id 5024 df-eprel 5029 df-po 5035 df-so 5036 df-fr 5073 df-we 5075 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-ord 5726 df-on 5727 df-lim 5728 df-suc 5729 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-om 7066 df-er 7742 df-en 7956 df-fin 7959 |
This theorem is referenced by: marypha1lem 8339 pwfseqlem4 9484 fsumcom2 14505 fprodcom2 14714 sylow2a 18034 ablfac1eu 18472 wspthnfi 26815 wspthnonfi 26818 clwwlksnfi 26913 qerclwwlksnfi 26950 fsumiunle 29575 hashreprin 30698 reprfi2 30701 hgt750lema 30735 tgoldbachgtde 30738 fprodcnlem 39831 cnrefiisplem 40055 sge0uzfsumgt 40661 hoidmvlelem1 40809 hoidmvlelem2 40810 hoidmvlelem3 40811 hoidmvlelem4 40812 hspmbllem1 40840 |
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