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Theorem bj-sbf4 31410
Description: Substitution has no effect on a bound variabe (non-freeness case); see sbf2 2180. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-sbf4  |-  ( [ y  /  x ] F/ x ph  <->  F/ x ph )

Proof of Theorem bj-sbf4
StepHypRef Expression
1 nfnf1 1958 . 2  |-  F/ x F/ x ph
21sbf 2178 1  |-  ( [ y  /  x ] F/ x ph  <->  F/ x ph )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 187   F/wnf 1661   [wsb 1790
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-12 1909  ax-13 2057
This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1658  df-nf 1662  df-sb 1791
This theorem is referenced by: (None)
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