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Theorem bj-sbf4 33178
Description: Substitution has no effect on a bound variabe (non-freeness case); see sbf2 2532. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-sbf4 ([𝑦 / 𝑥]Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜑)

Proof of Theorem bj-sbf4
StepHypRef Expression
1 nfnf1 2190 . 2 𝑥𝑥𝜑
21sbf 2530 1 ([𝑦 / 𝑥]Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 197  wnf 1859  [wsb 2052
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1873  ax-4 1888  ax-5 1994  ax-6 2060  ax-7 2096  ax-10 2177  ax-12 2206  ax-13 2411
This theorem depends on definitions:  df-bi 198  df-an 384  df-or 864  df-ex 1856  df-nf 1861  df-sb 2053
This theorem is referenced by: (None)
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