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Theorem sb9 2035
Description: Commutation of quantification and substitution variables. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sb9  |-  ( A. x [ x  /  y ] ph  <->  A. y [ y  /  x ] ph )

Proof of Theorem sb9
StepHypRef Expression
1 sb9i 2034 . 2  |-  ( A. x [ x  /  y ] ph  ->  A. y [ y  /  x ] ph )
2 sb9i 2034 . 2  |-  ( A. y [ y  /  x ] ph  ->  A. x [ x  /  y ] ph )
31, 2impbii 180 1  |-  ( A. x [ x  /  y ] ph  <->  A. y [ y  /  x ] ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 176   A.wal 1527   [wsb 1629
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630
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