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Mirrors > Home > ILE Home > Th. List > 3exdistr | Unicode version |
Description: Distribution of existential quantifiers. (Contributed by NM, 9-Mar-1995.) (Proof shortened by Andrew Salmon, 25-May-2011.) |
Ref | Expression |
---|---|
3exdistr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3anass 966 | . . . 4 | |
2 | 1 | 2exbii 1585 | . . 3 |
3 | 19.42vv 1883 | . . 3 | |
4 | exdistr 1881 | . . . 4 | |
5 | 4 | anbi2i 452 | . . 3 |
6 | 2, 3, 5 | 3bitri 205 | . 2 |
7 | 6 | exbii 1584 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 w3a 962 wex 1468 |
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 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-4 1487 ax-17 1506 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 df-3an 964 |
This theorem is referenced by: (None) |
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