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Mirrors > Home > ILE Home > Th. List > elrp | Unicode version |
Description: Membership in the set of positive reals. (Contributed by NM, 27-Oct-2007.) |
Ref | Expression |
---|---|
elrp |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq2 4004 |
. 2
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2 | df-rp 9638 |
. 2
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3 | 1, 2 | elrab2 2896 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-rab 2464 df-v 2739 df-un 3133 df-sn 3597 df-pr 3598 df-op 3600 df-br 4001 df-rp 9638 |
This theorem is referenced by: elrpii 9640 nnrp 9647 rpgt0 9649 rpregt0 9651 ralrp 9659 rexrp 9660 rpaddcl 9661 rpmulcl 9662 rpdivcl 9663 rpgecl 9666 rphalflt 9667 ge0p1rp 9669 rpnegap 9670 negelrp 9671 ltsubrp 9674 ltaddrp 9675 difrp 9676 elrpd 9677 iccdil 9982 icccntr 9984 dfrp2 10247 expgt0 10536 sqrtdiv 11032 mulcn2 11301 ef01bndlem 11745 nconstwlpolem 14461 |
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