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Theorem reueq 3275
 Description: Equality has existential uniqueness. (Contributed by Mario Carneiro, 1-Sep-2015.)
Assertion
Ref Expression
reueq
Distinct variable groups:   ,   ,

Proof of Theorem reueq
StepHypRef Expression
1 risset 2960 . 2
2 moeq 3253 . . . 4
3 mormo 3050 . . . 4
42, 3ax-mp 5 . . 3
5 reu5 3051 . . 3
64, 5mpbiran2 927 . 2
71, 6bitr4i 255 1
 Colors of variables: wff setvar class Syntax hints:   wb 187   wceq 1437   wcel 1870  wmo 2267  wrex 2783  wreu 2784  wrmo 2785 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-eu 2270  df-mo 2271  df-clab 2415  df-cleq 2421  df-clel 2424  df-rex 2788  df-reu 2789  df-rmo 2790  df-v 3089 This theorem is referenced by:  icoshftf1o  11753
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