Theorem exisym1 36652

Description: A symmetry with ∃.

See negsym1 36645 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 2161	. 2 ⊢ Ⅎ𝑥∃𝑥𝜑
2		falim 1564	. . 3 ⊢ (⊥ → 𝜑)
3	2	eximi 1842	. 2 ⊢ (∃𝑥⊥ → ∃𝑥𝜑)
4	1, 3	exlimi 2229	1 ⊢ (∃𝑥∃𝑥⊥ → ∃𝑥𝜑)

Syntax hints:   → wi 4  ⊥wfal 1559  ∃wex 1786

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-10 2152  ax-12 2189

This theorem depends on definitions:  df-bi 208  df-tru 1550  df-fal 1560  df-ex 1787  df-nf 1791

This theorem is referenced by: (None)