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Theorem dfsb7 2058
 Description: An alternate definition of proper substitution df-sb 1630. 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 2039, first for then for . Compare Definition 2.1'' of [Quine] p. 17, which is obtained from this theorem by applying df-clab 2270. Theorem sb7h 2060 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 2039 . . 3
21sbbii 1634 . 2
3 nfv 1605 . . 3
43sbco2 2026 . 2
5 sb5 2039 . 2
62, 4, 53bitr3i 266 1
 Colors of variables: wff set class Syntax hints:   wb 176   wa 358  wex 1528  wsb 1629 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630
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