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Mirrors > Home > ILE Home > Th. List > sbcom2v | Unicode version |
Description: Lemma for proving sbcom2 1987. It is the same as sbcom2 1987 but with
additional distinct variable constraints on ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
sbcom2v |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alcom 1478 |
. . 3
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2 | bi2.04 248 |
. . . . . 6
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3 | 2 | albii 1470 |
. . . . 5
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4 | 19.21v 1873 |
. . . . 5
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5 | 3, 4 | bitri 184 |
. . . 4
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6 | 5 | albii 1470 |
. . 3
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7 | 19.21v 1873 |
. . . 4
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8 | 7 | albii 1470 |
. . 3
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9 | 1, 6, 8 | 3bitr3i 210 |
. 2
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10 | sb6 1886 |
. . 3
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11 | sb6 1886 |
. . . . 5
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12 | 11 | imbi2i 226 |
. . . 4
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13 | 12 | albii 1470 |
. . 3
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14 | 10, 13 | bitri 184 |
. 2
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15 | sb6 1886 |
. . 3
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16 | sb6 1886 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
17 | 16 | imbi2i 226 |
. . . 4
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18 | 17 | albii 1470 |
. . 3
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19 | 15, 18 | bitri 184 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | 9, 14, 19 | 3bitr4i 212 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-11 1506 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 |
This theorem depends on definitions: df-bi 117 df-sb 1763 |
This theorem is referenced by: sbcom2v2 1986 |
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