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Theorem exisym1 34613
Description: A symmetry with .

See negsym1 34606 for more information. (Contributed by Anthony Hart, 4-Sep-2011.)

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

Proof of Theorem exisym1
StepHypRef Expression
1 nfe1 2147 . 2 𝑥𝑥𝜑
2 falim 1556 . . 3 (⊥ → 𝜑)
32eximi 1837 . 2 (∃𝑥⊥ → ∃𝑥𝜑)
41, 3exlimi 2210 1 (∃𝑥𝑥⊥ → ∃𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wfal 1551  wex 1782
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-10 2137  ax-12 2171
This theorem depends on definitions:  df-bi 206  df-tru 1542  df-fal 1552  df-ex 1783  df-nf 1787
This theorem is referenced by: (None)
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