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Theorem dfsb7 2079
 Description: An alternate definition of proper substitution df-sb 1883. 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 1993, first for then for . Compare Definition 2.1'' of [Quine] p. 17, which is obtained from this theorem by applying df-clab 2240. Theorem sb7h 2081 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 1993 . . 3
21sbbii 1885 . 2
3 nfv 1629 . . 3
43sbco2 1980 . 2
5 sb5 1993 . 2
62, 4, 53bitr3i 268 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360  wex 1537   wceq 1619  wsb 1882 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883
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