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Mirrors > Home > ILE Home > Th. List > dfsb7 | Unicode version |
Description: An alternate definition of proper substitution df-sb 1646. By introducing a dummy variable in the definiens, we are able to eliminate any distinct variable restrictions among the variables , , and of the definiendum. No distinct variable conflicts arise because effectively insulates from . To achieve this, we use a chain of two substitutions in the form of sb5 1767, first for then for . Compare Definition 2.1'' of [Quine] p. 17. Theorem sb7f 1868 provides a version where and don't have to be distinct. (Contributed by NM, 28-Jan-2004.) |
Ref | Expression |
---|---|
dfsb7 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb5 1767 | . . 3 | |
2 | 1 | sbbii 1648 | . 2 |
3 | ax-17 1419 | . . 3 | |
4 | 3 | sbco2v 1821 | . 2 |
5 | sb5 1767 | . 2 | |
6 | 2, 4, 5 | 3bitr3i 199 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wb 98 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-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: (None) |
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