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Theorem unqsym1 36408
Description: A symmetry with ∃!.

See negsym1 36400 for more information. (Contributed by Anthony Hart, 6-Sep-2011.)

Assertion
Ref Expression
unqsym1 (∃!𝑥∃!𝑥⊥ → ∃!𝑥𝜑)

Proof of Theorem unqsym1
StepHypRef Expression
1 neufal 36389 . . . 4 ¬ ∃!𝑥
21nex 1797 . . 3 ¬ ∃𝑥∃!𝑥
3 euex 2575 . . 3 (∃!𝑥∃!𝑥⊥ → ∃𝑥∃!𝑥⊥)
42, 3mto 197 . 2 ¬ ∃!𝑥∃!𝑥
54pm2.21i 119 1 (∃!𝑥∃!𝑥⊥ → ∃!𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wfal 1549  wex 1776  ∃!weu 2566
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-fal 1550  df-ex 1777  df-eu 2567
This theorem is referenced by: (None)
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