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Theorem bj-sbf4 32505
Description: Substitution has no effect on a bound variabe (non-freeness case); see sbf2 2381. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-sbf4 ([𝑦 / 𝑥]Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜑)

Proof of Theorem bj-sbf4
StepHypRef Expression
1 nfnf1 2028 . 2 𝑥𝑥𝜑
21sbf 2379 1 ([𝑦 / 𝑥]Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 196  wnf 1705  [wsb 1877
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-10 2016  ax-12 2044  ax-13 2245
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1702  df-nf 1707  df-sb 1878
This theorem is referenced by: (None)
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