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Mirrors > Home > ILE Home > Th. List > pm13.183 | Unicode version |
Description: Compare theorem *13.183 in [WhiteheadRussell] p. 178. Only is required to be a set. (Contributed by Andrew Salmon, 3-Jun-2011.) |
Ref | Expression |
---|---|
pm13.183 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq1 2087 | . 2 | |
2 | eqeq2 2090 | . . . 4 | |
3 | 2 | bibi1d 231 | . . 3 |
4 | 3 | albidv 1745 | . 2 |
5 | eqeq2 2090 | . . . 4 | |
6 | 5 | alrimiv 1795 | . . 3 |
7 | stdpc4 1698 | . . . 4 | |
8 | sbbi 1874 | . . . . 5 | |
9 | eqsb3 2182 | . . . . . . 7 | |
10 | 9 | bibi2i 225 | . . . . . 6 |
11 | equsb1 1708 | . . . . . . 7 | |
12 | bi1 116 | . . . . . . 7 | |
13 | 11, 12 | mpi 15 | . . . . . 6 |
14 | 10, 13 | sylbi 119 | . . . . 5 |
15 | 8, 14 | sylbi 119 | . . . 4 |
16 | 7, 15 | syl 14 | . . 3 |
17 | 6, 16 | impbii 124 | . 2 |
18 | 1, 4, 17 | vtoclbg 2659 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 wal 1282 wceq 1284 wcel 1433 wsb 1685 |
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-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 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-clel 2077 df-nfc 2208 df-v 2603 |
This theorem is referenced by: mpt22eqb 5630 |
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