Theorem bnj1239

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

	Ref	Expression
Assertion	bnj1239	⊢ ( ∃ 𝑥 ∈ 𝐴 ( 𝜓 ∧ 𝜒 ) → ∃ 𝑥 ∈ 𝐴 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		simpl	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜓 )
2	1	reximi	⊢ ( ∃ 𝑥 ∈ 𝐴 ( 𝜓 ∧ 𝜒 ) → ∃ 𝑥 ∈ 𝐴 𝜓 )