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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 388 |
. . 3
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2 | 1 | sbbii 1775 |
. 2
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3 | sbim 1963 |
. . . 4
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4 | sbim 1963 |
. . . 4
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5 | 3, 4 | anbi12i 460 |
. . 3
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6 | sban 1965 |
. . 3
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7 | dfbi2 388 |
. . 3
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8 | 5, 6, 7 | 3bitr4i 212 |
. 2
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9 | 2, 8 | bitri 184 |
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-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 |
This theorem depends on definitions: df-bi 117 df-nf 1471 df-sb 1773 |
This theorem is referenced by: sblbis 1970 sbrbis 1971 sbco 1978 sbcocom 1980 sb8eu 2049 sb8euh 2059 elsb1 2165 elsb2 2166 pm13.183 2887 sbcbig 3021 sb8iota 5197 |
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