Theorem bnj1397

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypotheses	bnj1397.1	⊢ ( 𝜑 → ∃ 𝑥 𝜓 )
	bnj1397.2	⊢ ( 𝜓 → ∀ 𝑥 𝜓 )
Assertion	bnj1397	⊢ ( 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		bnj1397.1	⊢ ( 𝜑 → ∃ 𝑥 𝜓 )
2		bnj1397.2	⊢ ( 𝜓 → ∀ 𝑥 𝜓 )
3	2	19.9h	⊢ ( ∃ 𝑥 𝜓 ↔ 𝜓 )
4	1 3	sylib	⊢ ( 𝜑 → 𝜓 )