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Theorem sbid2h 1777
Description: An identity law for substitution. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
sbid2h.1  |-  ( ph  ->  A. x ph )
Assertion
Ref Expression
sbid2h  |-  ( [ y  /  x ] [ x  /  y ] ph  <->  ph )

Proof of Theorem sbid2h
StepHypRef Expression
1 sbid2h.1 . . 3  |-  ( ph  ->  A. x ph )
21sbcof2 1738 . 2  |-  ( [ y  /  x ] [ x  /  y ] ph  <->  [ y  /  x ] ph )
31sbh 1706 . 2  |-  ( [ y  /  x ] ph 
<-> 
ph )
42, 3bitri 182 1  |-  ( [ y  /  x ] [ x  /  y ] ph  <->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103   A.wal 1287   [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:  sbid2  1778  sb5rf  1780  sb6rf  1781  sbid2v  1920
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