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Mirrors > Home > ILE Home > Th. List > resqrexlem1arp | Unicode version |
Description: Lemma for resqrex 10447. ![]() ![]() ![]() |
Ref | Expression |
---|---|
resqrexlem1arp.a |
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resqrexlem1arp.agt0 |
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Ref | Expression |
---|---|
resqrexlem1arp |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1red 7493 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | resqrexlem1arp.a |
. . . . . 6
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3 | 2 | adantr 270 |
. . . . 5
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4 | 1, 3 | readdcld 7507 |
. . . 4
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5 | 0lt1 7600 |
. . . . . 6
![]() ![]() ![]() ![]() | |
6 | 5 | a1i 9 |
. . . . 5
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7 | resqrexlem1arp.agt0 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | 7 | adantr 270 |
. . . . 5
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9 | addgtge0 7918 |
. . . . 5
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10 | 1, 3, 6, 8, 9 | syl22anc 1175 |
. . . 4
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11 | 4, 10 | elrpd 9161 |
. . 3
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12 | fvconst2g 5503 |
. . 3
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13 | 11, 12 | sylancom 411 |
. 2
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14 | 13, 11 | eqeltrd 2164 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 579 ax-in2 580 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-13 1449 ax-14 1450 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-sep 3955 ax-pow 4007 ax-pr 4034 ax-un 4258 ax-setind 4351 ax-cnex 7426 ax-resscn 7427 ax-1cn 7428 ax-1re 7429 ax-icn 7430 ax-addcl 7431 ax-addrcl 7432 ax-mulcl 7433 ax-addcom 7435 ax-addass 7437 ax-i2m1 7440 ax-0lt1 7441 ax-0id 7443 ax-rnegex 7444 ax-pre-ltwlin 7448 ax-pre-ltadd 7451 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-fal 1295 df-nf 1395 df-sb 1693 df-eu 1951 df-mo 1952 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ne 2256 df-nel 2351 df-ral 2364 df-rex 2365 df-rab 2368 df-v 2621 df-sbc 2841 df-dif 3001 df-un 3003 df-in 3005 df-ss 3012 df-pw 3429 df-sn 3450 df-pr 3451 df-op 3453 df-uni 3652 df-br 3844 df-opab 3898 df-mpt 3899 df-id 4118 df-xp 4442 df-rel 4443 df-cnv 4444 df-co 4445 df-dm 4446 df-rn 4447 df-iota 4975 df-fun 5012 df-fn 5013 df-f 5014 df-fv 5018 df-ov 5647 df-pnf 7514 df-mnf 7515 df-xr 7516 df-ltxr 7517 df-le 7518 df-rp 9125 |
This theorem is referenced by: resqrexlemf 10428 resqrexlemf1 10429 resqrexlemfp1 10430 |
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