Theorem exisym1 33292

Description: A symmetry with ∃.

See negsym1 33285 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 2087	. 2 ⊢ Ⅎ𝑥∃𝑥𝜑
2		falim 1524	. . 3 ⊢ (⊥ → 𝜑)
3	2	eximi 1797	. 2 ⊢ (∃𝑥⊥ → ∃𝑥𝜑)
4	1, 3	exlimi 2147	1 ⊢ (∃𝑥∃𝑥⊥ → ∃𝑥𝜑)

Syntax hints:   → wi 4  ⊥wfal 1519  ∃wex 1742

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-10 2079  ax-12 2106

This theorem depends on definitions:  df-bi 199  df-tru 1510  df-fal 1520  df-ex 1743  df-nf 1747

This theorem is referenced by: (None)