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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 2253 |
. . . 4
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2 | 1 | notbid 668 |
. . 3
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3 | 2 | rabbidv 2741 |
. 2
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4 | dfdif2 3152 |
. 2
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5 | dfdif2 3152 |
. 2
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6 | 3, 4, 5 | 3eqtr4g 2247 |
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 615 ax-in2 616 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-11 1517 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-ral 2473 df-rab 2477 df-dif 3146 |
This theorem is referenced by: difeq12 3263 difeq2i 3265 difeq2d 3268 disjdif2 3516 ssdifeq0 3520 2oconcl 6464 diffitest 6915 diffifi 6922 undifdc 6952 sbthlem2 6987 isbth 6996 difinfinf 7130 ismkvnex 7183 iscld 14063 |
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