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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 982 |
. . . 4
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2 | 1 | 2exbii 1606 |
. . 3
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3 | 19.42vv 1911 |
. . 3
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4 | exdistr 1909 |
. . . 4
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5 | 4 | anbi2i 457 |
. . 3
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6 | 2, 3, 5 | 3bitri 206 |
. 2
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7 | 6 | exbii 1605 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1447 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-4 1510 ax-17 1526 ax-ial 1534 |
This theorem depends on definitions: df-bi 117 df-3an 980 |
This theorem is referenced by: (None) |
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