Theorem exisym1 36992

Description: A symmetry with ∃.

See negsym1 36985 for more information. (Contributed by Anthony Hart, 4-Sep-2011.)

Assertion

Ref	Expression
exisym1	⊢ (∃𝑥∃𝑥⊥ → ∃𝑥𝜑)

Proof of Theorem exisym1

Step	Hyp	Ref	Expression
1		nfe1 2188	. 2 ⊢ Ⅎ𝑥∃𝑥𝜑
2		falim 1587	. . 3 ⊢ (⊥ → 𝜑)
3	2	eximi 1868	. 2 ⊢ (∃𝑥⊥ → ∃𝑥𝜑)
4	1, 3	exlimi 2256	1 ⊢ (∃𝑥∃𝑥⊥ → ∃𝑥𝜑)

This proof depends on syntax axioms:   → wi 4  ⊥wfal 1582  ∃wex 1812

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-10 2179  ax-12 2216

This proof depends on definitions:  df-bi 210  df-tru 1573  df-fal 1583  df-ex 1813  df-nf 1817

This theorem is used by: (None)