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Theorem rmov 3520
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 3143 . 2 (∃*𝑥 ∈ V 𝜑 ↔ ∃*𝑥(𝑥 ∈ V ∧ 𝜑))
2 vex 3495 . . . 4 𝑥 ∈ V
32biantrur 531 . . 3 (𝜑 ↔ (𝑥 ∈ V ∧ 𝜑))
43mobii 2624 . 2 (∃*𝑥𝜑 ↔ ∃*𝑥(𝑥 ∈ V ∧ 𝜑))
51, 4bitr4i 279 1 (∃*𝑥 ∈ V 𝜑 ↔ ∃*𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 207  wa 396  wcel 2105  ∃*wmo 2613  ∃*wrmo 3138  Vcvv 3492
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1772  df-sb 2061  df-mo 2615  df-clab 2797  df-cleq 2811  df-clel 2890  df-rmo 3143  df-v 3494
This theorem is referenced by: (None)
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