Theorem bnj534

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

	Ref	Expression
Hypothesis	bnj534.1	⊢ ( 𝜒 → ( ∃ 𝑥 𝜑 ∧ 𝜓 ) )
Assertion	bnj534	⊢ ( 𝜒 → ∃ 𝑥 ( 𝜑 ∧ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		bnj534.1	⊢ ( 𝜒 → ( ∃ 𝑥 𝜑 ∧ 𝜓 ) )
2		19.41v	⊢ ( ∃ 𝑥 ( 𝜑 ∧ 𝜓 ) ↔ ( ∃ 𝑥 𝜑 ∧ 𝜓 ) )
3	1 2	sylibr	⊢ ( 𝜒 → ∃ 𝑥 ( 𝜑 ∧ 𝜓 ) )