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Theorem exisym1 36407
Description: A symmetry with .

See negsym1 36400 for more information. (Contributed by Anthony Hart, 4-Sep-2011.)

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

Proof of Theorem exisym1
StepHypRef Expression
1 nfe1 2148 . 2 𝑥𝑥𝜑
2 falim 1554 . . 3 (⊥ → 𝜑)
32eximi 1832 . 2 (∃𝑥⊥ → ∃𝑥𝜑)
41, 3exlimi 2215 1 (∃𝑥𝑥⊥ → ∃𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wfal 1549  wex 1776
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  ax-7 2005  ax-10 2139  ax-12 2175
This theorem depends on definitions:  df-bi 207  df-tru 1540  df-fal 1550  df-ex 1777  df-nf 1781
This theorem is referenced by: (None)
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