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Mirrors > Home > ILE Home > Th. List > treq | Unicode version |
Description: Equality theorem for the transitive class predicate. (Contributed by NM, 17-Sep-1993.) |
Ref | Expression |
---|---|
treq |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unieq 3589 |
. . . 4
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2 | 1 | sseq1d 2972 |
. . 3
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3 | sseq2 2967 |
. . 3
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4 | 2, 3 | bitrd 177 |
. 2
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5 | df-tr 3855 |
. 2
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6 | df-tr 3855 |
. 2
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7 | 4, 5, 6 | 3bitr4g 212 |
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 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-in 2924 df-ss 2931 df-uni 3581 df-tr 3855 |
This theorem is referenced by: truni 3868 ordeq 4109 ordsucim 4226 ordom 4329 |
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