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Theorem dfsb7 1864
 Description: An alternate definition of proper substitution df-sb 1643. 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 1764, first for then for . Compare Definition 2.1'' of [Quine] p. 17. Theorem sb7f 1865 provides a version where and don't have to be distinct. (Contributed by NM, 28-Jan-2004.)
Assertion
Ref Expression
dfsb7
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)

Proof of Theorem dfsb7
StepHypRef Expression
1 sb5 1764 . . 3
21sbbii 1645 . 2
3 ax-17 1416 . . 3
43sbco2v 1818 . 2
5 sb5 1764 . 2
62, 4, 53bitr3i 199 1
 Colors of variables: wff set class Syntax hints:   wa 97   wb 98  wex 1378  wsb 1642 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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643 This theorem is referenced by: (None)
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