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Theorem sb9 1855
 Description: Commutation of quantification and substitution variables. (Contributed by NM, 5-Aug-1993.) (Proof rewritten by Jim Kingdon, 23-Mar-2018.)
Assertion
Ref Expression
sb9

Proof of Theorem sb9
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sb9v 1854 . . 3
2 sbcom 1849 . . . 4
32albii 1359 . . 3
4 sb9v 1854 . . 3
51, 3, 43bitri 195 . 2
6 ax-17 1419 . . . 4
76sbco2h 1838 . . 3
87albii 1359 . 2
96sbco2h 1838 . . 3
109albii 1359 . 2
115, 8, 103bitr3ri 200 1
 Colors of variables: wff set class Syntax hints:   wb 98  wal 1241  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:  sb9i  1856
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