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Mirrors > Home > HSE Home > Th. List > leopg | Unicode version |
Description: Ordering relation for positive operators. Definition of positive operator ordering in [Kreyszig] p. 470. (Contributed by NM, 23-Jul-2006.) (New usage is discouraged.) |
Ref | Expression |
---|---|
leopg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq2 6048 |
. . . 4
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2 | 1 | eleq1d 2470 |
. . 3
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3 | 1 | fveq1d 5689 |
. . . . . 6
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4 | 3 | oveq1d 6055 |
. . . . 5
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5 | 4 | breq2d 4184 |
. . . 4
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6 | 5 | ralbidv 2686 |
. . 3
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7 | 2, 6 | anbi12d 692 |
. 2
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8 | oveq1 6047 |
. . . 4
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9 | 8 | eleq1d 2470 |
. . 3
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10 | 8 | fveq1d 5689 |
. . . . . 6
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11 | 10 | oveq1d 6055 |
. . . . 5
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12 | 11 | breq2d 4184 |
. . . 4
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13 | 12 | ralbidv 2686 |
. . 3
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14 | 9, 13 | anbi12d 692 |
. 2
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15 | df-leop 23308 |
. 2
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16 | 7, 14, 15 | brabg 4434 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem is referenced by: leop 23579 leoprf2 23583 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1552 ax-5 1563 ax-17 1623 ax-9 1662 ax-8 1683 ax-14 1725 ax-6 1740 ax-7 1745 ax-11 1757 ax-12 1946 ax-ext 2385 ax-sep 4290 ax-nul 4298 ax-pr 4363 |
This theorem depends on definitions: df-bi 178 df-or 360 df-an 361 df-3an 938 df-tru 1325 df-ex 1548 df-nf 1551 df-sb 1656 df-eu 2258 df-mo 2259 df-clab 2391 df-cleq 2397 df-clel 2400 df-nfc 2529 df-ne 2569 df-ral 2671 df-rex 2672 df-rab 2675 df-v 2918 df-dif 3283 df-un 3285 df-in 3287 df-ss 3294 df-nul 3589 df-if 3700 df-sn 3780 df-pr 3781 df-op 3783 df-uni 3976 df-br 4173 df-opab 4227 df-iota 5377 df-fv 5421 df-ov 6043 df-leop 23308 |
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