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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3anass 934 |
. . . 4
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2 | 1 | 2exbii 1553 |
. . 3
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3 | 19.42vv 1848 |
. . 3
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4 | exdistr 1846 |
. . . 4
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5 | 4 | anbi2i 448 |
. . 3
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6 | 2, 3, 5 | 3bitri 205 |
. 2
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7 | 6 | exbii 1552 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1391 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-4 1455 ax-17 1474 ax-ial 1482 |
This theorem depends on definitions: df-bi 116 df-3an 932 |
This theorem is referenced by: (None) |
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