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Metamath Proof Explorer

Theorem mptex

Description: If the domain of a function given by maps-to notation is a set, the function is a set. Inference version of mptexg . (Contributed by NM, 22-Apr-2005) (Revised by Mario Carneiro, 20-Dec-2013)

Ref Expression
Hypothesis mptex.1 ⊢ A ∈ V
Assertion mptex ⊢ x ∈ A ⟼ B ∈ V

Proof

Step Hyp Ref Expression
1 mptex.1 ⊢ A ∈ V
2 mptexg ⊢ A ∈ V → x ∈ A ⟼ B ∈ V
3 1 2 ax-mp ⊢ x ∈ A ⟼ B ∈ V