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Mirrors > Home > ILE Home > Th. List > weeq2 | Unicode version |
Description: Equality theorem for the well-ordering predicate. (Contributed by NM, 3-Apr-1994.) |
Ref | Expression |
---|---|
weeq2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | freq2 4173 |
. . 3
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2 | raleq 2562 |
. . . . 5
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3 | 2 | raleqbi1dv 2570 |
. . . 4
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4 | 3 | raleqbi1dv 2570 |
. . 3
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5 | 1, 4 | anbi12d 457 |
. 2
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6 | df-wetr 4161 |
. 2
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7 | df-wetr 4161 |
. 2
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8 | 5, 6, 7 | 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-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ral 2364 df-in 3005 df-ss 3012 df-frfor 4158 df-frind 4159 df-wetr 4161 |
This theorem is referenced by: reg3exmid 4395 |
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