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 )