Theorem bj-hbex

Description: A more general instance of hbex . (Contributed by BJ, 4-Apr-2026)

	Ref	Expression
Hypothesis	bj-hbex.1	⊢ ( 𝜑 → ∀ 𝑥 𝜓 )
Assertion	bj-hbex	⊢ ( ∃ 𝑦 𝜑 → ∀ 𝑥 ∃ 𝑦 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		bj-hbex.1	⊢ ( 𝜑 → ∀ 𝑥 𝜓 )
2		19.12	⊢ ( ∃ 𝑦 ∀ 𝑥 𝜓 → ∀ 𝑥 ∃ 𝑦 𝜓 )
3	2 1	bj-sylge	⊢ ( ∃ 𝑦 𝜑 → ∀ 𝑥 ∃ 𝑦 𝜓 )