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Theorem sbid2v 1920
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 1464 . 2  |-  ( ph  ->  A. x ph )
21sbid2h 1777 1  |-  ( [ y  /  x ] [ x  /  y ] ph  <->  ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 103   [wsb 1692
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472
This theorem depends on definitions:  df-bi 115  df-sb 1693
This theorem is referenced by:  bdph  11387
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