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Mirrors > Home > ILE Home > Th. List > rext | Unicode version |
Description: A theorem similar to extensionality, requiring the existence of a singleton. Exercise 8 of [TakeutiZaring] p. 16. (Contributed by NM, 10-Aug-1993.) |
Ref | Expression |
---|---|
rext |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vsnid 3602 | . . 3 | |
2 | vex 2724 | . . . . 5 | |
3 | 2 | snex 4158 | . . . 4 |
4 | eleq2 2228 | . . . . 5 | |
5 | eleq2 2228 | . . . . 5 | |
6 | 4, 5 | imbi12d 233 | . . . 4 |
7 | 3, 6 | spcv 2815 | . . 3 |
8 | 1, 7 | mpi 15 | . 2 |
9 | velsn 3587 | . . 3 | |
10 | equcomi 1691 | . . 3 | |
11 | 9, 10 | sylbi 120 | . 2 |
12 | 8, 11 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1340 wceq 1342 wcel 2135 csn 3570 |
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-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 |
This theorem is referenced by: (None) |
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