Theorem exisym1 32423

Description: A symmetry with ∃.

See negsym1 32416 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 2027	. 2 ⊢ Ⅎ𝑥∃𝑥𝜑
2		falim 1498	. . 3 ⊢ (⊥ → 𝜑)
3	2	eximi 1762	. 2 ⊢ (∃𝑥⊥ → ∃𝑥𝜑)
4	1, 3	exlimi 2086	1 ⊢ (∃𝑥∃𝑥⊥ → ∃𝑥𝜑)

Syntax hints:   → wi 4  ⊥wfal 1488  ∃wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-tru 1486  df-fal 1489  df-ex 1705  df-nf 1710

This theorem is referenced by: (None)