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Theorem rmoeq 27801
 Description: Equality's restricted existential "at most one" property. (Contributed by Thierry Arnoux, 30-Mar-2018.)
Assertion
Ref Expression
rmoeq
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem rmoeq
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 id 22 . . . 4
21rgenw 2765 . . 3
3 eqeq2 2417 . . . . . 6
43imbi2d 314 . . . . 5
54ralbidv 2843 . . . 4
65spcegv 3145 . . 3
72, 6mpi 20 . 2
8 nfv 1728 . . 3
98rmo2 3366 . 2
107, 9sylibr 212 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1405  wex 1633   wcel 1842  wral 2754  wrmo 2757 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-eu 2242  df-mo 2243  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ral 2759  df-rmo 2762  df-v 3061 This theorem is referenced by: (None)
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