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Theorem rmoeq 3733
 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 3702 . . 3 ∃*𝑥 𝑥 = 𝐴
21moani 2635 . 2 ∃*𝑥(𝑥𝐵𝑥 = 𝐴)
3 df-rmo 3151 . 2 (∃*𝑥𝐵 𝑥 = 𝐴 ↔ ∃*𝑥(𝑥𝐵𝑥 = 𝐴))
42, 3mpbir 232 1 ∃*𝑥𝐵 𝑥 = 𝐴
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 396   = wceq 1530   ∈ wcel 2107  ∃*wmo 2618  ∃*wrmo 3146 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 1904  ax-6 1963  ax-7 2008  ax-9 2117  ax-ext 2798 This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1774  df-mo 2620  df-cleq 2819  df-rmo 3151 This theorem is referenced by:  nbusgredgeu  27081
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