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Mirrors > Home > ILE Home > Th. List > sneqd | Unicode version |
Description: Equality deduction for singletons. (Contributed by NM, 22-Jan-2004.) |
Ref | Expression |
---|---|
sneqd.1 |
Ref | Expression |
---|---|
sneqd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sneqd.1 | . 2 | |
2 | sneq 3409 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1284 csn 3398 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-11 1437 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-sn 3404 |
This theorem is referenced by: dmsnsnsng 4818 cnvsng 4826 ressn 4878 f1osng 5187 fsng 5357 fnressn 5370 fvsng 5380 2nd1st 5826 dfmpt2 5864 cnvf1olem 5865 tpostpos 5902 tfrlemi1 5969 en1bg 6303 xpassen 6327 fztp 9095 fzsuc2 9096 fseq1p1m1 9111 fseq1m1p1 9112 divalgmod 10327 |
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