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Theorem reueq 2732
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 2346 . 2
2 moeq 2710 . . . 4
3 mormo 2515 . . . 4
42, 3ax-mp 7 . . 3
5 reu5 2516 . . 3
64, 5mpbiran2 847 . 2
71, 6bitr4i 176 1
Colors of variables: wff set class
Syntax hints:   wb 98   wceq 1242   wcel 1390  wmo 1898  wrex 2301  wreu 2302  wrmo 2303
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901  df-clab 2024  df-cleq 2030  df-clel 2033  df-rex 2306  df-reu 2307  df-rmo 2308  df-v 2553
This theorem is referenced by:  divfnzn  8332  icoshftf1o  8629
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