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Metamath Proof Explorer

Theorem issetf

Description: A version of isset that does not require x and A to be distinct. (Contributed by Andrew Salmon, 6-Jun-2011) (Revised by Mario Carneiro, 10-Oct-2016)

Ref Expression
Hypothesis issetf.1 ⊢ Ⅎ _ x A
Assertion issetf ⊢ A ∈ V ↔ ∃ x x = A

Proof

Step Hyp Ref Expression
1 issetf.1 ⊢ Ⅎ _ x A
2 issetft ⊢ Ⅎ _ x A → A ∈ V ↔ ∃ x x = A
3 1 2 ax-mp ⊢ A ∈ V ↔ ∃ x x = A