Theorem amosym1 37338

Description: A symmetry with ∃*.

See negsym1 37329 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 37321	. . 3 ⊢ ∃*𝑥⊥
2	1	a1i 11	. 2 ⊢ (𝜑 → ∃*𝑥⊥)
3	2	moimi 2570	1 ⊢ (∃*𝑥∃*𝑥⊥ → ∃*𝑥𝜑)

This proof depends on syntax axioms:   → wi 4  ⊥wfal 1581  ∃*wmo 2562

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1572  df-fal 1582  df-ex 1812  df-mo 2564

This theorem is used by: (None)