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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 2151 |
. . . 4
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2 | 1 | notbid 627 |
. . 3
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3 | 2 | rabbidv 2608 |
. 2
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4 | dfdif2 3007 |
. 2
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5 | dfdif2 3007 |
. 2
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6 | 3, 4, 5 | 3eqtr4g 2145 |
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 ax-in1 579 ax-in2 580 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-11 1442 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-ral 2364 df-rab 2368 df-dif 3001 |
This theorem is referenced by: difeq12 3113 difeq2i 3115 difeq2d 3118 disjdif2 3361 ssdifeq0 3365 2oconcl 6203 diffitest 6603 diffifi 6610 undifdc 6634 sbthlem2 6667 isbth 6676 |
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