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Theorem bj-sbf3 36225
Description: Substitution has no effect on a bound variable (existential quantifier case); see sbf2 2255. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-sbf3 ([𝑦 / 𝑥]∃𝑥𝜑 ↔ ∃𝑥𝜑)

Proof of Theorem bj-sbf3
StepHypRef Expression
1 nfe1 2139 . 2 𝑥𝑥𝜑
21sbf 2254 1 ([𝑦 / 𝑥]∃𝑥𝜑 ↔ ∃𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 205  wex 1773  [wsb 2059
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-10 2129  ax-12 2163
This theorem depends on definitions:  df-bi 206  df-ex 1774  df-nf 1778  df-sb 2060
This theorem is referenced by: (None)
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