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Mirrors > Home > ILE Home > Th. List > dcned | Unicode version |
Description: Decidable equality implies decidable negated equality. (Contributed by Jim Kingdon, 3-May-2020.) |
Ref | Expression |
---|---|
dcned.eq | DECID |
Ref | Expression |
---|---|
dcned | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dcned.eq | . . 3 DECID | |
2 | dcn 827 | . . 3 DECID DECID | |
3 | 1, 2 | syl 14 | . 2 DECID |
4 | df-ne 2309 | . . 3 | |
5 | 4 | dcbii 825 | . 2 DECID DECID |
6 | 3, 5 | sylibr 133 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 DECID wdc 819 wceq 1331 wne 2308 |
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 |
This theorem depends on definitions: df-bi 116 df-dc 820 df-ne 2309 |
This theorem is referenced by: nn0n0n1ge2b 9130 algcvgblem 11730 |
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