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Theorem rmoeq 3732
Description: Equality's restricted existential "at most one" property. (Contributed by Thierry Arnoux, 30-Mar-2018.) (Revised by AV, 27-Oct-2020.) (Proof shortened by NM, 29-Oct-2020.)
Assertion
Ref Expression
rmoeq ∃*𝑥𝐵 𝑥 = 𝐴
Distinct variable group:   𝑥,𝐴
Allowed substitution hint:   𝐵(𝑥)

Proof of Theorem rmoeq
StepHypRef Expression
1 moeq 3701 . . 3 ∃*𝑥 𝑥 = 𝐴
21moani 2543 . 2 ∃*𝑥(𝑥𝐵𝑥 = 𝐴)
3 df-rmo 3372 . 2 (∃*𝑥𝐵 𝑥 = 𝐴 ↔ ∃*𝑥(𝑥𝐵𝑥 = 𝐴))
42, 3mpbir 230 1 ∃*𝑥𝐵 𝑥 = 𝐴
Colors of variables: wff setvar class
Syntax hints:  wa 395   = wceq 1534  wcel 2099  ∃*wmo 2528  ∃*wrmo 3371
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-9 2109  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1775  df-mo 2530  df-cleq 2720  df-rmo 3372
This theorem is referenced by:  nbusgredgeu  29172
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