Theorem bnj1265

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

	Ref	Expression
Hypothesis	bnj1265.1	⊢ ( 𝜑 → ∃ 𝑥 ∈ 𝐴 𝜓 )
Assertion	bnj1265	⊢ ( 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		bnj1265.1	⊢ ( 𝜑 → ∃ 𝑥 ∈ 𝐴 𝜓 )
2	1	bnj1196	⊢ ( 𝜑 → ∃ 𝑥 ( 𝑥 ∈ 𝐴 ∧ 𝜓 ) )
3	2	bnj1266	⊢ ( 𝜑 → ∃ 𝑥 𝜓 )
4	3	bnj937	⊢ ( 𝜑 → 𝜓 )