Users' Mathboxes Mathbox for Anthony Hart < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  exisym1 Structured version   Visualization version   GIF version

Theorem exisym1 34251
Description: A symmetry with .

See negsym1 34244 for more information. (Contributed by Anthony Hart, 4-Sep-2011.)

Assertion
Ref Expression
exisym1 (∃𝑥𝑥⊥ → ∃𝑥𝜑)

Proof of Theorem exisym1
StepHypRef Expression
1 nfe1 2155 . 2 𝑥𝑥𝜑
2 falim 1559 . . 3 (⊥ → 𝜑)
32eximi 1841 . 2 (∃𝑥⊥ → ∃𝑥𝜑)
41, 3exlimi 2219 1 (∃𝑥𝑥⊥ → ∃𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wfal 1554  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 1975  ax-7 2020  ax-10 2145  ax-12 2179
This theorem depends on definitions:  df-bi 210  df-tru 1545  df-fal 1555  df-ex 1787  df-nf 1791
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator