Theorem bnj31

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

	Ref	Expression
Hypotheses	bnj31.1	⊢ ( 𝜑 → ∃ 𝑥 ∈ 𝐴 𝜓 )
	bnj31.2	⊢ ( 𝜓 → 𝜒 )
Assertion	bnj31	⊢ ( 𝜑 → ∃ 𝑥 ∈ 𝐴 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		bnj31.1	⊢ ( 𝜑 → ∃ 𝑥 ∈ 𝐴 𝜓 )
2		bnj31.2	⊢ ( 𝜓 → 𝜒 )
3	2	reximi	⊢ ( ∃ 𝑥 ∈ 𝐴 𝜓 → ∃ 𝑥 ∈ 𝐴 𝜒 )
4	1 3	syl	⊢ ( 𝜑 → ∃ 𝑥 ∈ 𝐴 𝜒 )