Metamath Proof Explorer


Theorem uniexd

Description: Deduction version of the ZF Axiom of Union in class notation. (Contributed by Glauco Siliprandi, 26-Jun-2021)

Ref Expression
Hypothesis uniexd.1 ⊢ φ → A ∈ V
Assertion uniexd ⊢ φ → ⋃ A ∈ V

Proof

Step Hyp Ref Expression
1 uniexd.1 ⊢ φ → A ∈ V
2 uniexg ⊢ A ∈ V → ⋃ A ∈ V
3 1 2 syl ⊢ φ → ⋃ A ∈ V