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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 2831 | . 2 DECID DECID |
6 | eumo 2009 | . 2 | |
7 | 5, 6 | syl6 33 | 1 DECID DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wo 682 DECID wdc 804 w3o 946 wceq 1316 wcel 1465 weu 1977 wmo 1978 cvv 2660 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-dc 805 df-3or 948 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-v 2662 |
This theorem is referenced by: (None) |
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