Theorem bnj593

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

	Ref	Expression
Hypotheses	bnj593.1	⊢ ( 𝜑 → ∃ 𝑥 𝜓 )
	bnj593.2	⊢ ( 𝜓 → 𝜒 )
Assertion	bnj593	⊢ ( 𝜑 → ∃ 𝑥 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		bnj593.1	⊢ ( 𝜑 → ∃ 𝑥 𝜓 )
2		bnj593.2	⊢ ( 𝜓 → 𝜒 )
3	2	eximi	⊢ ( ∃ 𝑥 𝜓 → ∃ 𝑥 𝜒 )
4	1 3	syl	⊢ ( 𝜑 → ∃ 𝑥 𝜒 )