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Theorem sbid2h 1803
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 1764 . 2  |-  ( [ y  /  x ] [ x  /  y ] ph  <->  [ y  /  x ] ph )
31sbh 1732 . 2  |-  ( [ y  /  x ] ph 
<-> 
ph )
42, 3bitri 183 1  |-  ( [ y  /  x ] [ x  /  y ] ph  <->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   A.wal 1312   [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:  sbid2  1804  sb5rf  1806  sb6rf  1807  sbid2v  1947
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