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Theorem sbid2h 1771
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 1732 . 2  |-  ( [ y  /  x ] [ x  /  y ] ph  <->  [ y  /  x ] ph )
31sbh 1700 . 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 1283   [wsb 1686
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 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-sb 1687
This theorem is referenced by:  sbid2  1772  sb5rf  1774  sb6rf  1775  sbid2v  1914
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