Theorem exisym1 34613

Description: A symmetry with ∃.

See negsym1 34606 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 2147	. 2 ⊢ Ⅎ𝑥∃𝑥𝜑
2		falim 1556	. . 3 ⊢ (⊥ → 𝜑)
3	2	eximi 1837	. 2 ⊢ (∃𝑥⊥ → ∃𝑥𝜑)
4	1, 3	exlimi 2210	1 ⊢ (∃𝑥∃𝑥⊥ → ∃𝑥𝜑)

Syntax hints:   → wi 4  ⊥wfal 1551  ∃wex 1782

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-10 2137  ax-12 2171

This theorem depends on definitions:  df-bi 206  df-tru 1542  df-fal 1552  df-ex 1783  df-nf 1787

This theorem is referenced by: (None)