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Theorem sbid2 2160
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 sbco 2159 . 2  |-  ( [ y  /  x ] [ x  /  y ] ph  <->  [ y  /  x ] ph )
2 sbid2.1 . . 3  |-  F/ x ph
32sbf 2118 . 2  |-  ( [ y  /  x ] ph 
<-> 
ph )
41, 3bitri 242 1  |-  ( [ y  /  x ] [ x  /  y ] ph  <->  ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 178   F/wnf 1554   [wsb 1659
This theorem is referenced by:  sbco2  2162  sb5rf  2167  sb6rf  2168  sbid2v  2201
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660
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