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Theorem bj-sbf4 33314
Description: Substitution has no effect on a bound variabe (non-freeness case); see sbf2 2482. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-sbf4 ([𝑦 / 𝑥]Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜑)

Proof of Theorem bj-sbf4
StepHypRef Expression
1 nfnf1 2198 . 2 𝑥𝑥𝜑
21sbf 2479 1 ([𝑦 / 𝑥]Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 198  wnf 1879  [wsb 2064
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-10 2185  ax-12 2213  ax-13 2354
This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-ex 1876  df-nf 1880  df-sb 2065
This theorem is referenced by: (None)
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