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Theorem sbid2v 2083
Description: An identity law for substitution. Used in proof of Theorem 9.7 of [Megill] p. 449 (p. 16 of the preprint). (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sbid2v  |-  ( [ y  /  x ] [ x  /  y ] ph  <->  ph )
Distinct variable group:    ph, x
Allowed substitution hint:    ph( y)

Proof of Theorem sbid2v
StepHypRef Expression
1 nfv 1629 . 2  |-  F/ x ph
21sbid2 1978 1  |-  ( [ y  /  x ] [ x  /  y ] ph  <->  ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 178   [wsb 1882
This theorem is referenced by:  sbelx  2084
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 1883
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