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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 1841 | . . 3 | |
2 | 1 | anbi2i 452 | . 2 |
3 | df-sb 1721 | . 2 | |
4 | ax-4 1472 | . . 3 | |
5 | 4 | pm4.71ri 389 | . 2 |
6 | 2, 3, 5 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1314 wex 1453 wsb 1720 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1408 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-11 1469 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 |
This theorem depends on definitions: df-bi 116 df-sb 1721 |
This theorem is referenced by: sb5 1843 sbnv 1844 sbanv 1845 sbi1v 1847 sbi2v 1848 hbs1 1891 2sb6 1937 sbcom2v 1938 sb6a 1941 sb7af 1946 sbalyz 1952 sbal1yz 1954 exsb 1961 sbal2 1975 |
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