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Mirrors > Home > ILE Home > Th. List > poeq1 | Unicode version |
Description: Equality theorem for partial ordering predicate. (Contributed by NM, 27-Mar-1997.) |
Ref | Expression |
---|---|
poeq1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq 3939 |
. . . . . 6
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2 | 1 | notbid 657 |
. . . . 5
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3 | breq 3939 |
. . . . . . 7
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4 | breq 3939 |
. . . . . . 7
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5 | 3, 4 | anbi12d 465 |
. . . . . 6
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6 | breq 3939 |
. . . . . 6
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7 | 5, 6 | imbi12d 233 |
. . . . 5
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8 | 2, 7 | anbi12d 465 |
. . . 4
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9 | 8 | ralbidv 2438 |
. . 3
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10 | 9 | 2ralbidv 2462 |
. 2
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11 | df-po 4226 |
. 2
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12 | df-po 4226 |
. 2
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13 | 10, 11, 12 | 3bitr4g 222 |
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-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-4 1488 ax-17 1507 ax-ial 1515 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-cleq 2133 df-clel 2136 df-ral 2422 df-br 3938 df-po 4226 |
This theorem is referenced by: soeq1 4245 |
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