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Mirrors > Home > ILE Home > Th. List > axsep2 | Unicode version |
Description: A less restrictive version of the Separation Scheme ax-sep 3875, where variables and can both appear free in the wff , which can therefore be thought of as . This version was derived from the more restrictive ax-sep 3875 with no additional set theory axioms. (Contributed by NM, 10-Dec-2006.) (Proof shortened by Mario Carneiro, 17-Nov-2016.) |
Ref | Expression |
---|---|
axsep2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq2 2101 | . . . . . . 7 | |
2 | 1 | anbi1d 438 | . . . . . 6 |
3 | anabs5 507 | . . . . . 6 | |
4 | 2, 3 | syl6bb 185 | . . . . 5 |
5 | 4 | bibi2d 221 | . . . 4 |
6 | 5 | albidv 1705 | . . 3 |
7 | 6 | exbidv 1706 | . 2 |
8 | ax-sep 3875 | . 2 | |
9 | 7, 8 | chvarv 1812 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wb 98 wal 1241 wex 1381 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-ext 2022 ax-sep 3875 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-cleq 2033 df-clel 2036 |
This theorem is referenced by: (None) |
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