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Mirrors > Home > ILE Home > Th. List > sbbi | Unicode version |
Description: Equivalence inside and outside of a substitution are equivalent. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
sbbi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfbi2 381 |
. . 3
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2 | 1 | sbbii 1702 |
. 2
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3 | sbim 1882 |
. . . 4
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4 | sbim 1882 |
. . . 4
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5 | 3, 4 | anbi12i 449 |
. . 3
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6 | sban 1884 |
. . 3
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7 | dfbi2 381 |
. . 3
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8 | 5, 6, 7 | 3bitr4i 211 |
. 2
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9 | 2, 8 | bitri 183 |
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-io 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-4 1452 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 |
This theorem depends on definitions: df-bi 116 df-nf 1402 df-sb 1700 |
This theorem is referenced by: sblbis 1889 sbrbis 1890 sbco 1897 sbcocom 1899 elsb3 1907 elsb4 1908 sb8eu 1968 sb8euh 1978 pm13.183 2768 sbcbig 2899 sb8iota 5021 |
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