Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 2904 | . 2 DECID DECID |
6 | eumo 2051 | . 2 | |
7 | 5, 6 | syl6 33 | 1 DECID DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wo 703 DECID wdc 829 w3o 972 wceq 1348 weu 2019 wmo 2020 wcel 2141 cvv 2730 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-dc 830 df-3or 974 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-v 2732 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |