Metamath Proof Explorer


Theorem exisym1

Description: A symmetry with E. .

See negsym1 for more information. (Contributed by Anthony Hart, 4-Sep-2011)

Ref Expression
Assertion exisym1 ⊢ ∃ x ∃ x ⊥ → ∃ x φ

Proof

Step Hyp Ref Expression
1 nfe1 ⊢ Ⅎ x ∃ x φ
2 falim ⊢ ⊥ → φ
3 2 eximi ⊢ ∃ x ⊥ → ∃ x φ
4 1 3 exlimi ⊢ ∃ x ∃ x ⊥ → ∃ x φ