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Mirrors > Home > MPE Home > Th. List > prnmax | Structured version Unicode version |
Description: A positive real has no largest member. Definition 9-3.1(iii) of [Gleason] p. 121. (Contributed by NM, 9-Mar-1996.) (Revised by Mario Carneiro, 11-May-2013.) (New usage is discouraged.) |
Ref | Expression |
---|---|
prnmax |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2526 |
. . . . 5
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2 | 1 | anbi2d 703 |
. . . 4
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3 | breq1 4402 |
. . . . 5
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4 | 3 | rexbidv 2864 |
. . . 4
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5 | 2, 4 | imbi12d 320 |
. . 3
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6 | elnpi 9267 |
. . . . . 6
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7 | 6 | simprbi 464 |
. . . . 5
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8 | 7 | r19.21bi 2918 |
. . . 4
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9 | 8 | simprd 463 |
. . 3
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10 | 5, 9 | vtoclg 3134 |
. 2
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11 | 10 | anabsi7 815 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-ne 2649 df-ral 2803 df-rex 2804 df-rab 2807 df-v 3078 df-dif 3438 df-un 3440 df-in 3442 df-ss 3449 df-pss 3451 df-nul 3745 df-if 3899 df-sn 3985 df-pr 3987 df-op 3991 df-br 4400 df-np 9260 |
This theorem is referenced by: npomex 9275 prnmadd 9276 genpnmax 9286 1idpr 9308 ltexprlem4 9318 reclem3pr 9328 suplem1pr 9331 |
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