Metamath Proof Explorer


Theorem bnj1265

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

Ref Expression
Hypothesis bnj1265.1 ⊢ φ → ∃ x ∈ A ψ
Assertion bnj1265 ⊢ φ → ψ

Proof

Step Hyp Ref Expression
1 bnj1265.1 ⊢ φ → ∃ x ∈ A ψ
2 1 bnj1196 ⊢ φ → ∃ x x ∈ A ∧ ψ
3 2 bnj1266 ⊢ φ → ∃ x ψ
4 3 bnj937 ⊢ φ → ψ