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Theorem moeq3dc 2717
 Description: "At most one" property of equality (split into 3 cases). (Contributed by Jim Kingdon, 7-Jul-2018.)
Hypotheses
Ref Expression
moeq3dc.1
moeq3dc.2
moeq3dc.3
moeq3dc.4
Assertion
Ref Expression
moeq3dc DECID DECID
Distinct variable groups:   ,   ,   ,   ,   ,

Proof of Theorem moeq3dc
StepHypRef Expression
1 moeq3dc.1 . . 3
2 moeq3dc.2 . . 3
3 moeq3dc.3 . . 3
4 moeq3dc.4 . . 3
51, 2, 3, 4eueq3dc 2715 . 2 DECID DECID
6 eumo 1932 . 2
75, 6syl6 29 1 DECID DECID
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 97   wo 629  DECID wdc 742   w3o 884   wceq 1243   wcel 1393  weu 1900  wmo 1901  cvv 2557 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-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-dc 743  df-3or 886  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-clab 2027  df-cleq 2033  df-clel 2036  df-v 2559 This theorem is referenced by: (None)
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