Theorem amosym1 36965

Description: A symmetry with ∃*.

See negsym1 36956 for more information. (Contributed by Anthony Hart, 13-Sep-2011.)

Assertion

Ref	Expression
amosym1	⊢ (∃*𝑥∃*𝑥⊥ → ∃*𝑥𝜑)

Proof of Theorem amosym1

Step	Hyp	Ref	Expression
1		mofal 36948	. . 3 ⊢ ∃*𝑥⊥
2	1	a1i 11	. 2 ⊢ (𝜑 → ∃*𝑥⊥)
3	2	moimi 2572	1 ⊢ (∃*𝑥∃*𝑥⊥ → ∃*𝑥𝜑)

This proof depends on syntax axioms:   → wi 4  ⊥wfal 1581  ∃*wmo 2564

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1572  df-fal 1582  df-ex 1809  df-mo 2566

This theorem is used by: (None)