Theorem exisym1 37308

Description: A symmetry with ∃.

See negsym1 37301 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 2186	. 2 ⊢ Ⅎ𝑥∃𝑥𝜑
2		falim 1586	. . 3 ⊢ (⊥ → 𝜑)
3	2	eximi 1867	. 2 ⊢ (∃𝑥⊥ → ∃𝑥𝜑)
4	1, 3	exlimi 2253	1 ⊢ (∃𝑥∃𝑥⊥ → ∃𝑥𝜑)

This proof depends on syntax axioms:   → wi 4  ⊥wfal 1581  ∃wex 1811

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-10 2177  ax-12 2212

This proof depends on definitions:  df-bi 210  df-tru 1572  df-fal 1582  df-ex 1812  df-nf 1816

This theorem is used by: (None)