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Theorem sb7af 1869
 Description: An alternative definition of proper substitution df-sb 1646. Similar to dfsb7a 1870 but does not require that and be distinct. Similar to sb7f 1868 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 1766 . . 3
21sbbii 1648 . 2
3 sb7af.1 . . 3
43sbco2 1839 . 2
5 sb6 1766 . 2
62, 4, 53bitr3i 199 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98  wal 1241  wnf 1349  wsb 1645 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646 This theorem is referenced by:  dfsb7a  1870
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