Users' Mathboxes Mathbox for Anthony Hart < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  amosym1 Structured version   Visualization version   GIF version

Theorem amosym1 36409
Description: A symmetry with ∃*.

See negsym1 36400 for more information. (Contributed by Anthony Hart, 13-Sep-2011.)

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

Proof of Theorem amosym1
StepHypRef Expression
1 mofal 36392 . . 3 ∃*𝑥
21a1i 11 . 2 (𝜑 → ∃*𝑥⊥)
32moimi 2543 1 (∃*𝑥∃*𝑥⊥ → ∃*𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wfal 1549  ∃*wmo 2536
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965
This theorem depends on definitions:  df-bi 207  df-or 848  df-tru 1540  df-fal 1550  df-ex 1777  df-mo 2538
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator