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Mirrors > Home > ILE Home > Th. List > frforeq3 | Unicode version |
Description: Equality theorem for the well-founded predicate. (Contributed by Jim Kingdon, 22-Sep-2021.) |
Ref | Expression |
---|---|
frforeq3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq2 2204 |
. . . . . . 7
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2 | 1 | imbi2d 229 |
. . . . . 6
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3 | 2 | ralbidv 2438 |
. . . . 5
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4 | eleq2 2204 |
. . . . 5
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5 | 3, 4 | imbi12d 233 |
. . . 4
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6 | 5 | ralbidv 2438 |
. . 3
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7 | sseq2 3126 |
. . 3
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8 | 6, 7 | imbi12d 233 |
. 2
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9 | df-frfor 4261 |
. 2
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10 | df-frfor 4261 |
. 2
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11 | 8, 9, 10 | 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-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-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-ral 2422 df-in 3082 df-ss 3089 df-frfor 4261 |
This theorem is referenced by: frind 4282 |
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