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Theorem sb7af 1911
 Description: An alternate definition of proper substitution df-sb 1687. Similar to dfsb7a 1912 but does not require that and be distinct. Similar to sb7f 1910 in that it involves a dummy variable , but expressed in terms of rather than . (Contributed by Jim Kingdon, 5-Feb-2018.)
Hypothesis
Ref Expression
sb7af.1
Assertion
Ref Expression
sb7af
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)

Proof of Theorem sb7af
StepHypRef Expression
1 sb6 1808 . . 3
21sbbii 1689 . 2
3 sb7af.1 . . 3
43sbco2 1881 . 2
5 sb6 1808 . 2
62, 4, 53bitr3i 208 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103  wal 1283  wnf 1390  wsb 1686 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469 This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687 This theorem is referenced by:  dfsb7a  1912
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