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Mirrors > Home > ILE Home > Th. List > difeq2 | Unicode version |
Description: Equality theorem for class difference. (Contributed by NM, 10-Feb-1997.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
difeq2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq2 2204 |
. . . 4
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2 | 1 | notbid 657 |
. . 3
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3 | 2 | rabbidv 2678 |
. 2
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4 | dfdif2 3084 |
. 2
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5 | dfdif2 3084 |
. 2
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6 | 3, 4, 5 | 3eqtr4g 2198 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-11 1485 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-ral 2422 df-rab 2426 df-dif 3078 |
This theorem is referenced by: difeq12 3194 difeq2i 3196 difeq2d 3199 disjdif2 3446 ssdifeq0 3450 2oconcl 6344 diffitest 6789 diffifi 6796 undifdc 6820 sbthlem2 6854 isbth 6863 difinfinf 6994 ismkvnex 7037 iscld 12311 |
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