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Mirrors > Home > ILE Home > Th. List > snfig | Unicode version |
Description: A singleton is finite. For the proper class case, see snprc 3657. (Contributed by Jim Kingdon, 13-Apr-2020.) |
Ref | Expression |
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snfig |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1onn 6520 |
. . 3
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2 | ensn1g 6796 |
. . 3
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3 | breq2 4007 |
. . . 4
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4 | 3 | rspcev 2841 |
. . 3
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5 | 1, 2, 4 | sylancr 414 |
. 2
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6 | isfi 6760 |
. 2
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7 | 5, 6 | sylibr 134 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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-in1 614 ax-in2 615 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 4121 ax-nul 4129 ax-pow 4174 ax-pr 4209 ax-un 4433 |
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-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-nul 3423 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-int 3845 df-br 4004 df-opab 4065 df-id 4293 df-suc 4371 df-iom 4590 df-xp 4632 df-rel 4633 df-cnv 4634 df-co 4635 df-dm 4636 df-rn 4637 df-fun 5218 df-fn 5219 df-f 5220 df-f1 5221 df-fo 5222 df-f1o 5223 df-1o 6416 df-en 6740 df-fin 6742 |
This theorem is referenced by: fiprc 6814 ssfiexmid 6875 domfiexmid 6877 diffitest 6886 unfiexmid 6916 prfidisj 6925 tpfidisj 6926 ssfii 6972 infpwfidom 7196 hashsng 10773 fihashen1 10774 hashunsng 10782 hashprg 10783 hashdifsn 10794 hashdifpr 10795 hashxp 10801 fsumsplitsnun 11422 fsum2dlemstep 11437 fisumcom2 11441 fsumconst 11457 fsumge1 11464 fsum00 11465 hash2iun1dif1 11483 fprod2dlemstep 11625 fprodcom2fi 11629 fprodsplitsn 11636 fprodsplit1f 11637 phicl2 12208 |
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