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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 2715 | . 2 DECID DECID |
6 | eumo 1932 | . 2 | |
7 | 5, 6 | syl6 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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