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Theorem rmov 3375
Description: An at-most-one quantifier restricted to the universe is unrestricted. (Contributed by Alexander van der Vekens, 17-Jun-2017.)
Assertion
Ref Expression
rmov (∃*𝑥 ∈ V 𝜑 ↔ ∃*𝑥𝜑)

Proof of Theorem rmov
StepHypRef Expression
1 df-rmo 3063 . 2 (∃*𝑥 ∈ V 𝜑 ↔ ∃*𝑥(𝑥 ∈ V ∧ 𝜑))
2 vex 3353 . . . 4 𝑥 ∈ V
32biantrur 526 . . 3 (𝜑 ↔ (𝑥 ∈ V ∧ 𝜑))
43mobii 2568 . 2 (∃*𝑥𝜑 ↔ ∃*𝑥(𝑥 ∈ V ∧ 𝜑))
51, 4bitr4i 269 1 (∃*𝑥 ∈ V 𝜑 ↔ ∃*𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 197  wa 384  wcel 2155  ∃*wmo 2563  ∃*wrmo 3058  Vcvv 3350
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2070  ax-7 2105  ax-9 2164  ax-12 2211  ax-ext 2743
This theorem depends on definitions:  df-bi 198  df-an 385  df-tru 1656  df-ex 1875  df-sb 2063  df-mo 2565  df-clab 2752  df-cleq 2758  df-clel 2761  df-rmo 3063  df-v 3352
This theorem is referenced by: (None)
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