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Metamath Proof Explorer

Theorem elfvexd

Description: If a function value has a member, then its argument is a set. Deduction form of elfvex . (An artifact of our function value definition.) (Contributed by David Moews, 1-May-2017)

Ref Expression
Hypothesis elfvexd.1 ⊢ φ → A ∈ B ⁡ C
Assertion elfvexd ⊢ φ → C ∈ V

Proof

Step Hyp Ref Expression
1 elfvexd.1 ⊢ φ → A ∈ B ⁡ C
2 elfvex ⊢ A ∈ B ⁡ C → C ∈ V
3 1 2 syl ⊢ φ → C ∈ V