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Mirrors > Home > ILE Home > Th. List > frforeq1 | Unicode version |
Description: Equality theorem for the well-founded predicate. (Contributed by Jim Kingdon, 22-Sep-2021.) |
Ref | Expression |
---|---|
frforeq1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq 3845 |
. . . . . . 7
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2 | 1 | imbi1d 229 |
. . . . . 6
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3 | 2 | ralbidv 2380 |
. . . . 5
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4 | 3 | imbi1d 229 |
. . . 4
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5 | 4 | ralbidv 2380 |
. . 3
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6 | 5 | imbi1d 229 |
. 2
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7 | df-frfor 4156 |
. 2
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8 | df-frfor 4156 |
. 2
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9 | 6, 7, 8 | 3bitr4g 221 |
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-5 1381 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-4 1445 ax-17 1464 ax-ial 1472 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-nf 1395 df-cleq 2081 df-clel 2084 df-ral 2364 df-br 3844 df-frfor 4156 |
This theorem is referenced by: freq1 4169 |
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