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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 1750. (Contributed by NM, 14-Apr-2008.) |
Ref | Expression |
---|---|
sb56 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hba1 1527 | . 2 | |
2 | ax11v 1814 | . . 3 | |
3 | ax-4 1497 | . . . 4 | |
4 | 3 | com12 30 | . . 3 |
5 | 2, 4 | impbid 128 | . 2 |
6 | 1, 5 | equsex 1715 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1340 wex 1479 |
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 1434 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-11 1493 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: sb6 1873 sb5 1874 alexeq 2847 dfdif3 3227 |
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