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Theorem sbid2 1843
Description: An identity law for substitution. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 6-Oct-2016.)
Hypothesis
Ref Expression
sbid2.1  |-  F/ x ph
Assertion
Ref Expression
sbid2  |-  ( [ y  /  x ] [ x  /  y ] ph  <->  ph )

Proof of Theorem sbid2
StepHypRef Expression
1 sbid2.1 . . 3  |-  F/ x ph
21nfri 1512 . 2  |-  ( ph  ->  A. x ph )
32sbid2h 1842 1  |-  ( [ y  /  x ] [ x  /  y ] ph  <->  ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 104   F/wnf 1453   [wsb 1755
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 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-11 1499  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527
This theorem depends on definitions:  df-bi 116  df-nf 1454  df-sb 1756
This theorem is referenced by:  sbco4lem  1999
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