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Theorem rmov 3208
Description: A uniqueness 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 2915 . 2 (∃*𝑥 ∈ V 𝜑 ↔ ∃*𝑥(𝑥 ∈ V ∧ 𝜑))
2 vex 3189 . . . 4 𝑥 ∈ V
32biantrur 527 . . 3 (𝜑 ↔ (𝑥 ∈ V ∧ 𝜑))
43mobii 2492 . 2 (∃*𝑥𝜑 ↔ ∃*𝑥(𝑥 ∈ V ∧ 𝜑))
51, 4bitr4i 267 1 (∃*𝑥 ∈ V 𝜑 ↔ ∃*𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 384  wcel 1987  ∃*wmo 2470  ∃*wrmo 2910  Vcvv 3186
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-12 2044  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-eu 2473  df-mo 2474  df-clab 2608  df-cleq 2614  df-clel 2617  df-rmo 2915  df-v 3188
This theorem is referenced by: (None)
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