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Theorem bj-sbf3 33401
Description: Substitution has no effect on a bound variabe (existential quantifier case); see sbf2 2457. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-sbf3 ([𝑦 / 𝑥]∃𝑥𝜑 ↔ ∃𝑥𝜑)

Proof of Theorem bj-sbf3
StepHypRef Expression
1 nfe1 2143 . 2 𝑥𝑥𝜑
21sbf 2455 1 ([𝑦 / 𝑥]∃𝑥𝜑 ↔ ∃𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 198  wex 1823  [wsb 2011
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2054  ax-10 2134  ax-12 2162  ax-13 2333
This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1824  df-nf 1828  df-sb 2012
This theorem is referenced by: (None)
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