Theorem bnj1131

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

	Ref	Expression
Hypotheses	bnj1131.1	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
	bnj1131.2	⊢ ∃ 𝑥 𝜑
Assertion	bnj1131	⊢ 𝜑

Proof

Step	Hyp	Ref	Expression
1		bnj1131.1	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
2		bnj1131.2	⊢ ∃ 𝑥 𝜑
3	1	19.9h	⊢ ( ∃ 𝑥 𝜑 ↔ 𝜑 )
4	2 3	mpbi	⊢ 𝜑