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| Description: A singleton is finite. For the proper class case, see snprc 3697. (Contributed by Jim Kingdon, 13-Apr-2020.) |
| Ref | Expression |
|---|---|
| snfig |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 1onn 6605 |
. . 3
| |
| 2 | ensn1g 6888 |
. . 3
| |
| 3 | breq2 4047 |
. . . 4
| |
| 4 | 3 | rspcev 2876 |
. . 3
|
| 5 | 1, 2, 4 | sylancr 414 |
. 2
|
| 6 | isfi 6851 |
. 2
| |
| 7 | 5, 6 | sylibr 134 |
1
|
| 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 615 ax-in2 616 ax-io 710 ax-5 1469 ax-7 1470 ax-gen 1471 ax-ie1 1515 ax-ie2 1516 ax-8 1526 ax-10 1527 ax-11 1528 ax-i12 1529 ax-bndl 1531 ax-4 1532 ax-17 1548 ax-i9 1552 ax-ial 1556 ax-i5r 1557 ax-13 2177 ax-14 2178 ax-ext 2186 ax-sep 4161 ax-nul 4169 ax-pow 4217 ax-pr 4252 ax-un 4479 |
| This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1375 df-nf 1483 df-sb 1785 df-eu 2056 df-mo 2057 df-clab 2191 df-cleq 2197 df-clel 2200 df-nfc 2336 df-ral 2488 df-rex 2489 df-v 2773 df-dif 3167 df-un 3169 df-in 3171 df-ss 3178 df-nul 3460 df-pw 3617 df-sn 3638 df-pr 3639 df-op 3641 df-uni 3850 df-int 3885 df-br 4044 df-opab 4105 df-id 4339 df-suc 4417 df-iom 4638 df-xp 4680 df-rel 4681 df-cnv 4682 df-co 4683 df-dm 4684 df-rn 4685 df-fun 5272 df-fn 5273 df-f 5274 df-f1 5275 df-fo 5276 df-f1o 5277 df-1o 6501 df-en 6827 df-fin 6829 |
| This theorem is referenced by: fiprc 6906 ssfiexmid 6972 domfiexmid 6974 diffitest 6983 unfiexmid 7014 prfidisj 7023 prfidceq 7024 tpfidisj 7025 ssfii 7075 infpwfidom 7305 hashsng 10941 fihashen1 10942 hashunsng 10950 hashprg 10951 hashdifsn 10962 hashdifpr 10963 hashxp 10969 fsumsplitsnun 11701 fsum2dlemstep 11716 fisumcom2 11720 fsumconst 11736 fsumge1 11743 fsum00 11744 hash2iun1dif1 11762 fprod2dlemstep 11904 fprodcom2fi 11908 fprodsplitsn 11915 fprodsplit1f 11916 phicl2 12507 lgsquadlem2 15526 |
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