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Mirrors > Home > ILE Home > Th. List > ensn1g | Unicode version |
Description: A singleton is equinumerous to ordinal one. (Contributed by NM, 23-Apr-2004.) |
Ref | Expression |
---|---|
ensn1g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sneq 3571 | . . 3 | |
2 | 1 | breq1d 3976 | . 2 |
3 | vex 2715 | . . 3 | |
4 | 3 | ensn1 6742 | . 2 |
5 | 2, 4 | vtoclg 2772 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1335 wcel 2128 csn 3560 class class class wbr 3966 c1o 6357 cen 6684 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-13 2130 ax-14 2131 ax-ext 2139 ax-sep 4083 ax-nul 4091 ax-pow 4136 ax-pr 4170 ax-un 4394 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-nul 3395 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3774 df-br 3967 df-opab 4027 df-id 4254 df-suc 4332 df-xp 4593 df-rel 4594 df-cnv 4595 df-co 4596 df-dm 4597 df-rn 4598 df-fun 5173 df-fn 5174 df-f 5175 df-f1 5176 df-fo 5177 df-f1o 5178 df-1o 6364 df-en 6687 |
This theorem is referenced by: enpr1g 6744 en1bg 6746 en2sn 6759 snfig 6760 enpr2d 6763 snnen2og 6805 en1eqsn 6893 en1eqsnbi 6894 pr2nelem 7127 dju1en 7149 |
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