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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfbi2 368 | . . 3 | |
2 | 1 | sbbii 1648 | . 2 |
3 | sbim 1827 | . . . 4 | |
4 | sbim 1827 | . . . 4 | |
5 | 3, 4 | anbi12i 433 | . . 3 |
6 | sban 1829 | . . 3 | |
7 | dfbi2 368 | . . 3 | |
8 | 5, 6, 7 | 3bitr4i 201 | . 2 |
9 | 2, 8 | bitri 173 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wsb 1645 |
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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