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Mirrors > Home > ILE Home > Th. List > dfsb7 | Unicode version |
Description: An alternate definition of proper substitution df-sb 1736. 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 1859, first for then for . Compare Definition 2.1'' of [Quine] p. 17. Theorem sb7f 1965 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 1859 | . . 3 | |
2 | 1 | sbbii 1738 | . 2 |
3 | ax-17 1506 | . . 3 | |
4 | 3 | sbco2vh 1916 | . 2 |
5 | sb5 1859 | . 2 | |
6 | 2, 4, 5 | 3bitr3i 209 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wex 1468 wsb 1735 |
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-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 |
This theorem is referenced by: (None) |
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