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Mirrors > Home > ILE Home > Th. List > sbal1 | Unicode version |
Description: A theorem used in
elimination of disjoint variable conditions on
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Ref | Expression |
---|---|
sbal1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbal 2000 |
. . . 4
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2 | 1 | sbbii 1765 |
. . 3
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3 | sbal1yz 2001 |
. . 3
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4 | 2, 3 | bitrid 192 |
. 2
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5 | ax-17 1526 |
. . 3
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6 | 5 | sbco2vh 1945 |
. 2
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7 | ax-17 1526 |
. . . 4
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8 | 7 | sbco2vh 1945 |
. . 3
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9 | 8 | albii 1470 |
. 2
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10 | 4, 6, 9 | 3bitr3g 222 |
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-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-sb 1763 |
This theorem is referenced by: (None) |
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