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Mirrors > Home > ILE Home > Th. List > moeq3dc | Unicode version |
Description: "At most one" property of equality (split into 3 cases). (Contributed by Jim Kingdon, 7-Jul-2018.) |
Ref | Expression |
---|---|
moeq3dc.1 | |
moeq3dc.2 | |
moeq3dc.3 | |
moeq3dc.4 |
Ref | Expression |
---|---|
moeq3dc | DECID DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | moeq3dc.1 | . . 3 | |
2 | moeq3dc.2 | . . 3 | |
3 | moeq3dc.3 | . . 3 | |
4 | moeq3dc.4 | . . 3 | |
5 | 1, 2, 3, 4 | eueq3dc 2858 | . 2 DECID DECID |
6 | eumo 2031 | . 2 | |
7 | 5, 6 | syl6 33 | 1 DECID DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wo 697 DECID wdc 819 w3o 961 wceq 1331 wcel 1480 weu 1999 wmo 2000 cvv 2686 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-dc 820 df-3or 963 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-v 2688 |
This theorem is referenced by: (None) |
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