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Theorem reu0 4359
Description: Vacuous restricted uniqueness is always false. (Contributed by AV, 3-Apr-2023.)
Assertion
Ref Expression
reu0 ¬ ∃!𝑥 ∈ ∅ 𝜑

Proof of Theorem reu0
StepHypRef Expression
1 rex0 4358 . 2 ¬ ∃𝑥 ∈ ∅ 𝜑
2 reurex 3378 . 2 (∃!𝑥 ∈ ∅ 𝜑 → ∃𝑥 ∈ ∅ 𝜑)
31, 2mto 196 1 ¬ ∃!𝑥 ∈ ∅ 𝜑
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wrex 3068  ∃!wreu 3372  c0 4323
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1911  ax-6 1969  ax-7 2009  ax-8 2106  ax-9 2114  ax-ext 2701
This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1542  df-fal 1552  df-ex 1780  df-sb 2066  df-eu 2561  df-clab 2708  df-cleq 2722  df-clel 2808  df-ral 3060  df-rex 3069  df-rmo 3374  df-reu 3375  df-dif 3952  df-nul 4324
This theorem is referenced by:  join0  18364  meet0  18365
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