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Mirrors > Home > ILE Home > Th. List > zfun | Unicode version |
Description: Axiom of Union expressed with the fewest number of different variables. (Contributed by NM, 14-Aug-2003.) |
Ref | Expression |
---|---|
zfun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-un 4416 | . 2 | |
2 | elequ2 2146 | . . . . . . 7 | |
3 | elequ1 2145 | . . . . . . 7 | |
4 | 2, 3 | anbi12d 470 | . . . . . 6 |
5 | 4 | cbvexv 1911 | . . . . 5 |
6 | 5 | imbi1i 237 | . . . 4 |
7 | 6 | albii 1463 | . . 3 |
8 | 7 | exbii 1598 | . 2 |
9 | 1, 8 | mpbi 144 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1346 wex 1485 |
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-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-13 2143 ax-14 2144 ax-un 4416 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: uniex2 4419 bj-uniex2 13873 |
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