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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 368 |
. . 3
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2 | 1 | sbbii 1648 |
. 2
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3 | sbim 1827 |
. . . 4
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4 | sbim 1827 |
. . . 4
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5 | 3, 4 | anbi12i 433 |
. . 3
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6 | sban 1829 |
. . 3
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7 | dfbi2 368 |
. . 3
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8 | 5, 6, 7 | 3bitr4i 201 |
. 2
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9 | 2, 8 | bitri 173 |
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 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 |
This theorem is referenced by: sblbis 1834 sbrbis 1835 sbco 1842 sbcocom 1844 elsb3 1852 elsb4 1853 sb8eu 1913 sb8euh 1923 pm13.183 2681 sbcbig 2809 sb8iota 4874 |
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