Theorem exisym1 36781

Description: A symmetry with ∃.

See negsym1 36774 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 2184	. 2 ⊢ Ⅎ𝑥∃𝑥𝜑
2		falim 1577	. . 3 ⊢ (⊥ → 𝜑)
3	2	eximi 1855	. 2 ⊢ (∃𝑥⊥ → ∃𝑥𝜑)
4	1, 3	exlimi 2252	1 ⊢ (∃𝑥∃𝑥⊥ → ∃𝑥𝜑)

Syntax hints:   → wi 4  ⊥wfal 1572  ∃wex 1799

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1815  ax-4 1829  ax-5 1930  ax-6 1987  ax-7 2028  ax-10 2175  ax-12 2212

This theorem depends on definitions:  df-bi 209  df-tru 1563  df-fal 1573  df-ex 1800  df-nf 1804

This theorem is referenced by: (None)