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Theorem sbid2 1979
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 1978 . 2  |-  ( [ y  /  x ] [ x  /  y ] ph  <->  [ y  /  x ] ph )
2 sbid2.1 . . 3  |-  F/ x ph
32sbf 1899 . 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 1539   [wsb 1883
This theorem is referenced by:  sbco2  1981  sb5rf  1985  sb6rf  1986  sbid2v  2086
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884
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