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Theorem sbid2h 1849
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 1810 . 2  |-  ( [ y  /  x ] [ x  /  y ] ph  <->  [ y  /  x ] ph )
31sbh 1776 . 2  |-  ( [ y  /  x ] ph 
<-> 
ph )
42, 3bitri 184 1  |-  ( [ y  /  x ] [ x  /  y ] ph  <->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 105   A.wal 1351   [wsb 1762
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534
This theorem depends on definitions:  df-bi 117  df-sb 1763
This theorem is referenced by:  sbid2  1850  sb5rf  1852  sb6rf  1853  sbid2v  1996
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