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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | freq2 4318 | . . 3 | |
2 | raleq 2659 | . . . . 5 | |
3 | 2 | raleqbi1dv 2667 | . . . 4 |
4 | 3 | raleqbi1dv 2667 | . . 3 |
5 | 1, 4 | anbi12d 465 | . 2 |
6 | df-wetr 4306 | . 2 | |
7 | df-wetr 4306 | . 2 | |
8 | 5, 6, 7 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1342 wral 2442 class class class wbr 3976 wfr 4300 wwe 4302 |
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-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-in 3117 df-ss 3124 df-frfor 4303 df-frind 4304 df-wetr 4306 |
This theorem is referenced by: reg3exmid 4551 |
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