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Theorem sb9 2173
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 2172 . 2  |-  ( A. x [ x  /  y ] ph  ->  A. y [ y  /  x ] ph )
2 sb9i 2172 . 2  |-  ( A. y [ y  /  x ] ph  ->  A. x [ x  /  y ] ph )
31, 2impbii 182 1  |-  ( A. x [ x  /  y ] ph  <->  A. y [ y  /  x ] ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 178   A.wal 1550   [wsb 1659
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660
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