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Theorem dfsb7 1967
 Description: An alternate definition of proper substitution df-sb 1737. 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 1860, first for then for . Compare Definition 2.1'' of [Quine] p. 17. Theorem sb7f 1968 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 1860 . . 3
21sbbii 1739 . 2
3 ax-17 1507 . . 3
43sbco2vh 1919 . 2
5 sb5 1860 . 2
62, 4, 53bitr3i 209 1
 Colors of variables: wff set class Syntax hints:   wa 103   wb 104  wex 1469  wsb 1736 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516 This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737 This theorem is referenced by: (None)
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