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Theorem exisym1 32398
Description: A symmetry with .

See negsym1 32391 for more information. (Contributed by Anthony Hart, 4-Sep-2011.)

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

Proof of Theorem exisym1
StepHypRef Expression
1 nfe1 2025 . 2 𝑥𝑥𝜑
2 falim 1496 . . 3 (⊥ → 𝜑)
32eximi 1760 . 2 (∃𝑥⊥ → ∃𝑥𝜑)
41, 3exlimi 2084 1 (∃𝑥𝑥⊥ → ∃𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wfal 1486  wex 1702
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-10 2017  ax-12 2045
This theorem depends on definitions:  df-bi 197  df-or 385  df-tru 1484  df-fal 1487  df-ex 1703  df-nf 1708
This theorem is referenced by: (None)
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