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Mirrors > Home > ILE Home > Th. List > eujust | Unicode version |
Description: A soundness justification theorem for df-eu 1903, showing that the definition is equivalent to itself with its dummy variable renamed. Note that and needn't be distinct variables. (Contributed by NM, 11-Mar-2010.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) |
Ref | Expression |
---|---|
eujust |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equequ2 1599 | . . . . 5 | |
2 | 1 | bibi2d 221 | . . . 4 |
3 | 2 | albidv 1705 | . . 3 |
4 | 3 | cbvexv 1795 | . 2 |
5 | equequ2 1599 | . . . . 5 | |
6 | 5 | bibi2d 221 | . . . 4 |
7 | 6 | albidv 1705 | . . 3 |
8 | 7 | cbvexv 1795 | . 2 |
9 | 4, 8 | bitri 173 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 98 wal 1241 wceq 1243 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-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: (None) |
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