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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 3508 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1316 csn 3497 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-11 1469 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-sn 3503 |
This theorem is referenced by: dmsnsnsng 4986 cnvsng 4994 ressn 5049 f1osng 5376 fsng 5561 fnressn 5574 fvsng 5584 2nd1st 6046 dfmpo 6088 cnvf1olem 6089 tpostpos 6129 tfrlemi1 6197 tfr1onlemaccex 6213 tfrcllemaccex 6226 elixpsn 6597 ixpsnf1o 6598 en1bg 6662 mapsnen 6673 xpassen 6692 fztp 9826 fzsuc2 9827 fseq1p1m1 9842 fseq1m1p1 9843 zfz1isolemsplit 10549 zfz1isolem1 10551 fsumm1 11153 divalgmod 11551 ennnfonelemg 11843 ennnfonelemp1 11846 ennnfonelem1 11847 ennnfonelemnn0 11862 setsvalg 11916 strsetsid 11919 txdis 12373 |
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