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Mirrors > Home > ILE Home > Th. List > ddifss | Unicode version |
Description: Double complement under universal class. In classical logic (or given an additional hypothesis, as in ddifnel 3146), this is equality rather than subset. (Contributed by Jim Kingdon, 24-Jul-2018.) |
Ref | Expression |
---|---|
ddifss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssv 3061 |
. 2
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2 | ssddif 3249 |
. 2
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3 | 1, 2 | mpbi 144 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 582 ax-in2 583 ax-io 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 |
This theorem depends on definitions: df-bi 116 df-tru 1299 df-nf 1402 df-sb 1700 df-clab 2082 df-cleq 2088 df-clel 2091 df-nfc 2224 df-v 2635 df-dif 3015 df-in 3019 df-ss 3026 |
This theorem is referenced by: ssindif0im 3361 difdifdirss 3386 |
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