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Theorem rmov 3494
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 3368 . 2 (∃*𝑥 ∈ V 𝜑 ↔ ∃*𝑥(𝑥 ∈ V ∧ 𝜑))
2 vex 3470 . . . 4 𝑥 ∈ V
32biantrur 530 . . 3 (𝜑 ↔ (𝑥 ∈ V ∧ 𝜑))
43mobii 2534 . 2 (∃*𝑥𝜑 ↔ ∃*𝑥(𝑥 ∈ V ∧ 𝜑))
51, 4bitr4i 278 1 (∃*𝑥 ∈ V 𝜑 ↔ ∃*𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 205  wa 395  wcel 2098  ∃*wmo 2524  ∃*wrmo 3367  Vcvv 3466
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1536  df-ex 1774  df-sb 2060  df-mo 2526  df-clab 2702  df-cleq 2716  df-clel 2802  df-rmo 3368  df-v 3468
This theorem is referenced by: (None)
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