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Theorem reueq 3131
 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 2753 . 2
2 moeq 3110 . . . 4
3 mormo 2920 . . . 4
42, 3ax-mp 8 . . 3
5 reu5 2921 . . 3
64, 5mpbiran2 886 . 2
71, 6bitr4i 244 1
 Colors of variables: wff set class Syntax hints:   wb 177   wceq 1652   wcel 1725  wmo 2282  wrex 2706  wreu 2707  wrmo 2708 This theorem is referenced by:  icoshftf1o  11020 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-rex 2711  df-reu 2712  df-rmo 2713  df-v 2958
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