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Theorem sb9i 1856
Description: Commutation of quantification and substitution variables. (Contributed by NM, 5-Aug-1993.) (Proof rewritten by Jim Kingdon, 23-Mar-2018.)
Assertion
Ref Expression
sb9i  |-  ( A. x [ x  /  y ] ph  ->  A. y [ y  /  x ] ph )

Proof of Theorem sb9i
StepHypRef Expression
1 sb9 1855 . 2  |-  ( A. x [ x  /  y ] ph  <->  A. y [ y  /  x ] ph )
21biimpi 113 1  |-  ( A. x [ x  /  y ] ph  ->  A. y [ y  /  x ] ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.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: (None)
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