Theorem amosym1 36427

Description: A symmetry with ∃*.

See negsym1 36418 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 36410	. . 3 ⊢ ∃*𝑥⊥
2	1	a1i 11	. 2 ⊢ (𝜑 → ∃*𝑥⊥)
3	2	moimi 2545	1 ⊢ (∃*𝑥∃*𝑥⊥ → ∃*𝑥𝜑)

Syntax hints:   → wi 4  ⊥wfal 1552  ∃*wmo 2538

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967

This theorem depends on definitions:  df-bi 207  df-or 849  df-tru 1543  df-fal 1553  df-ex 1780  df-mo 2540

This theorem is referenced by: (None)