| Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > ILE Home > Th. List > snfig | Unicode version | ||
| Description: A singleton is finite. For the proper class case, see snprc 3698. (Contributed by Jim Kingdon, 13-Apr-2020.) |
| Ref | Expression |
|---|---|
| snfig |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 1onn 6606 |
. . 3
| |
| 2 | ensn1g 6889 |
. . 3
| |
| 3 | breq2 4048 |
. . . 4
| |
| 4 | 3 | rspcev 2877 |
. . 3
|
| 5 | 1, 2, 4 | sylancr 414 |
. 2
|
| 6 | isfi 6852 |
. 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 711 ax-5 1470 ax-7 1471 ax-gen 1472 ax-ie1 1516 ax-ie2 1517 ax-8 1527 ax-10 1528 ax-11 1529 ax-i12 1530 ax-bndl 1532 ax-4 1533 ax-17 1549 ax-i9 1553 ax-ial 1557 ax-i5r 1558 ax-13 2178 ax-14 2179 ax-ext 2187 ax-sep 4162 ax-nul 4170 ax-pow 4218 ax-pr 4253 ax-un 4480 |
| This theorem depends on definitions: df-bi 117 df-3an 983 df-tru 1376 df-nf 1484 df-sb 1786 df-eu 2057 df-mo 2058 df-clab 2192 df-cleq 2198 df-clel 2201 df-nfc 2337 df-ral 2489 df-rex 2490 df-v 2774 df-dif 3168 df-un 3170 df-in 3172 df-ss 3179 df-nul 3461 df-pw 3618 df-sn 3639 df-pr 3640 df-op 3642 df-uni 3851 df-int 3886 df-br 4045 df-opab 4106 df-id 4340 df-suc 4418 df-iom 4639 df-xp 4681 df-rel 4682 df-cnv 4683 df-co 4684 df-dm 4685 df-rn 4686 df-fun 5273 df-fn 5274 df-f 5275 df-f1 5276 df-fo 5277 df-f1o 5278 df-1o 6502 df-en 6828 df-fin 6830 |
| This theorem is referenced by: fiprc 6907 ssfiexmid 6973 domfiexmid 6975 diffitest 6984 unfiexmid 7015 prfidisj 7024 prfidceq 7025 tpfidisj 7026 ssfii 7076 infpwfidom 7306 hashsng 10943 fihashen1 10944 hashunsng 10952 hashprg 10953 hashdifsn 10964 hashdifpr 10965 hashxp 10971 fsumsplitsnun 11730 fsum2dlemstep 11745 fisumcom2 11749 fsumconst 11765 fsumge1 11772 fsum00 11773 hash2iun1dif1 11791 fprod2dlemstep 11933 fprodcom2fi 11937 fprodsplitsn 11944 fprodsplit1f 11945 phicl2 12536 lgsquadlem2 15555 |
| Copyright terms: Public domain | W3C validator |