Theorem bj-sbf3

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

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

Proof

Step	Hyp	Ref	Expression
1		nfe1	⊢ Ⅎ 𝑥 ∃ 𝑥 𝜑
2	1	sbf	⊢ ( [ 𝑦 / 𝑥 ] ∃ 𝑥 𝜑 ↔ ∃ 𝑥 𝜑 )