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Theorem sbid2v 2062
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 1605 . 2  |-  F/ x ph
21sbid2 2024 1  |-  ( [ y  /  x ] [ x  /  y ] ph  <->  ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 176   [wsb 1629
This theorem is referenced by:  sbelx  2063
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630
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