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Theorem eueqi 3604
 Description: There exists a unique set equal to a given set. Inference associated with euequ 2669. See euequ 2669 in the case of a setvar. (Contributed by NM, 5-Apr-1995.)
Hypothesis
Ref Expression
eueqi.1 𝐴 ∈ V
Assertion
Ref Expression
eueqi ∃!𝑥 𝑥 = 𝐴
Distinct variable group:   𝑥,𝐴

Proof of Theorem eueqi
StepHypRef Expression
1 eueqi.1 . 2 𝐴 ∈ V
2 eueq 3602 . 2 (𝐴 ∈ V ↔ ∃!𝑥 𝑥 = 𝐴)
31, 2mpbi 222 1 ∃!𝑥 𝑥 = 𝐴
 Colors of variables: wff setvar class Syntax hints:   = wceq 1656   ∈ wcel 2164  ∃!weu 2639  Vcvv 3414 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-9 2173  ax-10 2192  ax-11 2207  ax-12 2220  ax-ext 2803 This theorem depends on definitions:  df-bi 199  df-an 387  df-or 879  df-tru 1660  df-ex 1879  df-nf 1883  df-sb 2068  df-mo 2605  df-eu 2640  df-clab 2812  df-cleq 2818  df-clel 2821  df-v 3416 This theorem is referenced by:  eueq2  3605  eueq3  3606  fsn  6657  bj-nuliota  33536
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