Theorem bj-sbf3 34708

Description: Substitution has no effect on a bound variable (existential quantifier case); see sbf2 2270. (Contributed by BJ, 2-May-2019.)

Assertion

Ref	Expression
bj-sbf3	⊢ ([𝑦 / 𝑥]∃𝑥𝜑 ↔ ∃𝑥𝜑)

Proof of Theorem bj-sbf3

Step	Hyp	Ref	Expression
1		nfe1 2153	. 2 ⊢ Ⅎ𝑥∃𝑥𝜑
2	1	sbf 2269	1 ⊢ ([𝑦 / 𝑥]∃𝑥𝜑 ↔ ∃𝑥𝜑)

Syntax hints:   ↔ wb 209  ∃wex 1787  [wsb 2072

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2018  ax-10 2143  ax-12 2177

This theorem depends on definitions:  df-bi 210  df-ex 1788  df-nf 1792  df-sb 2073

This theorem is referenced by: (None)