Theorem bj-biexex

Description: When ph is substituted for ps , both sides express a form of nonfreeness. (Contributed by BJ, 20-Oct-2019)

	Ref	Expression
Assertion	bj-biexex	⊢ ( ∀ 𝑥 ( 𝜑 → ∃ 𝑥 𝜓 ) ↔ ( ∃ 𝑥 𝜑 → ∃ 𝑥 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		nfe1	⊢ Ⅎ 𝑥 ∃ 𝑥 𝜓
2	1	19.23	⊢ ( ∀ 𝑥 ( 𝜑 → ∃ 𝑥 𝜓 ) ↔ ( ∃ 𝑥 𝜑 → ∃ 𝑥 𝜓 ) )