Theorem bnj1238

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

	Ref	Expression
Hypothesis	bnj1238.1	⊢ ( 𝜑 ↔ ∃ 𝑥 ∈ 𝐴 ( 𝜓 ∧ 𝜒 ) )
Assertion	bnj1238	⊢ ( 𝜑 → ∃ 𝑥 ∈ 𝐴 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		bnj1238.1	⊢ ( 𝜑 ↔ ∃ 𝑥 ∈ 𝐴 ( 𝜓 ∧ 𝜒 ) )
2		bnj1239	⊢ ( ∃ 𝑥 ∈ 𝐴 ( 𝜓 ∧ 𝜒 ) → ∃ 𝑥 ∈ 𝐴 𝜓 )
3	1 2	sylbi	⊢ ( 𝜑 → ∃ 𝑥 ∈ 𝐴 𝜓 )