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Theorem bj-sbf4 32952
Description: Substitution has no effect on a bound variabe (non-freeness case); see sbf2 2410. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-sbf4 ([𝑦 / 𝑥]Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜑)

Proof of Theorem bj-sbf4
StepHypRef Expression
1 nfnf1 2071 . 2 𝑥𝑥𝜑
21sbf 2408 1 ([𝑦 / 𝑥]Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 196  wnf 1748  [wsb 1937
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-10 2059  ax-12 2087  ax-13 2282
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1745  df-nf 1750  df-sb 1938
This theorem is referenced by: (None)
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