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Theorem bj-sbf4 36823
Description: Substitution has no effect on a bound variable (nonfreeness case); see sbf2 2270. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-sbf4 ([𝑦 / 𝑥]Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜑)

Proof of Theorem bj-sbf4
StepHypRef Expression
1 nfnf1 2152 . 2 𝑥𝑥𝜑
21sbf 2269 1 ([𝑦 / 𝑥]Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 206  wnf 1780  [wsb 2062
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-10 2139  ax-12 2175
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-ex 1777  df-nf 1781  df-sb 2063
This theorem is referenced by: (None)
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