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Mirrors > Home > ILE Home > Th. List > neqned | Unicode version |
Description: If it is not the case that two classes are equal, they are unequal. Converse of neneqd 2270. One-way deduction form of df-ne 2250. (Contributed by David Moews, 28-Feb-2017.) Allow a shortening of necon3bi 2299. (Revised by Wolf Lammen, 22-Nov-2019.) |
Ref | Expression |
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neqned.1 |
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Ref | Expression |
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neqned |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | neqned.1 |
. 2
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2 | df-ne 2250 |
. 2
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3 | 1, 2 | sylibr 132 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 |
This theorem depends on definitions: df-bi 115 df-ne 2250 |
This theorem is referenced by: neqne 2257 tfr1onlemsucaccv 6038 tfrcllemsucaccv 6051 djune 6676 flqltnz 9583 bezoutlemle 10777 eucalgval2 10815 eucalglt 10819 lcmval 10825 lcmcllem 10829 isprm2 10879 sqne2sq 10935 |
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