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Mirrors > Home > ILE Home > Th. List > sb6 | Unicode version |
Description: Equivalence for substitution. Compare Theorem 6.2 of [Quine] p. 40. Also proved as Lemmas 16 and 17 of [Tarski] p. 70. (Contributed by NM, 18-Aug-1993.) (Revised by NM, 14-Apr-2008.) |
Ref | Expression |
---|---|
sb6 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb56 1765 | . . 3 | |
2 | 1 | anbi2i 430 | . 2 |
3 | df-sb 1646 | . 2 | |
4 | ax-4 1400 | . . 3 | |
5 | 4 | pm4.71ri 372 | . 2 |
6 | 2, 3, 5 | 3bitr4i 201 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wex 1381 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-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-11 1397 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 df-sb 1646 |
This theorem is referenced by: sb5 1767 sbnv 1768 sbanv 1769 sbi1v 1771 sbi2v 1772 hbs1 1814 2sb6 1860 sbcom2v 1861 sb6a 1864 sb7af 1869 sbalyz 1875 sbal1yz 1877 exsb 1884 sbal2 1898 |
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