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Theorem sbid2v 1947
Description: An identity law for substitution. Used in proof of Theorem 9.7 of [Megill] p. 449 (p. 16 of the preprint). (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sbid2v  |-  ( [ y  /  x ] [ x  /  y ] ph  <->  ph )
Distinct variable group:    ph, x
Allowed substitution hint:    ph( y)

Proof of Theorem sbid2v
StepHypRef Expression
1 ax-17 1489 . 2  |-  ( ph  ->  A. x ph )
21sbid2h 1803 1  |-  ( [ y  /  x ] [ x  /  y ] ph  <->  ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 104   [wsb 1718
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-11 1467  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497
This theorem depends on definitions:  df-bi 116  df-sb 1719
This theorem is referenced by:  bdph  12882
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