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Mirrors > Home > MPE Home > Th. List > prnmax | Structured version Visualization 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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2689 | . . . . 5 | |
2 | 1 | anbi2d 740 | . . . 4 |
3 | breq1 4656 | . . . . 5 | |
4 | 3 | rexbidv 3052 | . . . 4 |
5 | 2, 4 | imbi12d 334 | . . 3 |
6 | elnpi 9810 | . . . . . 6 | |
7 | 6 | simprbi 480 | . . . . 5 |
8 | 7 | r19.21bi 2932 | . . . 4 |
9 | 8 | simprd 479 | . . 3 |
10 | 5, 9 | vtoclg 3266 | . 2 |
11 | 10 | anabsi7 860 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 w3a 1037 wal 1481 wceq 1483 wcel 1990 wral 2912 wrex 2913 cvv 3200 wpss 3575 c0 3915 class class class wbr 4653 cnq 9674 cltq 9680 cnp 9681 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-pss 3590 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-np 9803 |
This theorem is referenced by: npomex 9818 prnmadd 9819 genpnmax 9829 1idpr 9851 ltexprlem4 9861 reclem3pr 9871 suplem1pr 9874 |
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