Theorem bnj1266

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

	Ref	Expression
Hypothesis	bnj1266.1	⊢ ( 𝜒 → ∃ 𝑥 ( 𝜑 ∧ 𝜓 ) )
Assertion	bnj1266	⊢ ( 𝜒 → ∃ 𝑥 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		bnj1266.1	⊢ ( 𝜒 → ∃ 𝑥 ( 𝜑 ∧ 𝜓 ) )
2		simpr	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜓 )
3	1 2	bnj593	⊢ ( 𝜒 → ∃ 𝑥 𝜓 )