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Mirrors > Home > ILE Home > Th. List > sb56 | Unicode version |
Description: Two equivalent ways of expressing the proper substitution of for in , when and are distinct. Theorem 6.2 of [Quine] p. 40. The proof does not involve df-sb 1686. (Contributed by NM, 14-Apr-2008.) |
Ref | Expression |
---|---|
sb56 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hba1 1473 | . 2 | |
2 | ax11v 1748 | . . 3 | |
3 | ax-4 1440 | . . . 4 | |
4 | 3 | com12 30 | . . 3 |
5 | 2, 4 | impbid 127 | . 2 |
6 | 1, 5 | equsex 1656 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wal 1282 wex 1421 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-11 1437 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: sb6 1807 sb5 1808 alexeq 2721 |
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