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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 |
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Ref | Expression |
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dcned |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dcned.eq |
. . 3
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2 | dcn 842 |
. . 3
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3 | 1, 2 | syl 14 |
. 2
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4 | df-ne 2348 |
. . 3
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5 | 4 | dcbii 840 |
. 2
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6 | 3, 5 | sylibr 134 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 |
This theorem depends on definitions: df-bi 117 df-dc 835 df-ne 2348 |
This theorem is referenced by: nn0n0n1ge2b 9308 algcvgblem 12019 |
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