Theorem bnj1517

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

	Ref	Expression
Hypothesis	bnj1517.1	⊢ 𝐴 = { 𝑥 ∣ ( 𝜑 ∧ 𝜓 ) }
Assertion	bnj1517	⊢ ( 𝑥 ∈ 𝐴 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		bnj1517.1	⊢ 𝐴 = { 𝑥 ∣ ( 𝜑 ∧ 𝜓 ) }
2	1	bnj1436	⊢ ( 𝑥 ∈ 𝐴 → ( 𝜑 ∧ 𝜓 ) )
3	2	simprd	⊢ ( 𝑥 ∈ 𝐴 → 𝜓 )