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Mirrors > Home > ILE Home > Th. List > divalglemqt | Unicode version |
Description: Lemma for divalg 11846. The case involved in showing uniqueness. (Contributed by Jim Kingdon, 5-Dec-2021.) |
Ref | Expression |
---|---|
divalglemqt.d | |
divalglemqt.r | |
divalglemqt.s | |
divalglemqt.q | |
divalglemqt.t | |
divalglemqt.qt | |
divalglemqt.eq |
Ref | Expression |
---|---|
divalglemqt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | divalglemqt.qt | . . . 4 | |
2 | 1 | oveq1d 5851 | . . 3 |
3 | divalglemqt.q | . . . . 5 | |
4 | divalglemqt.d | . . . . 5 | |
5 | 3, 4 | zmulcld 9310 | . . . 4 |
6 | 5 | zcnd 9305 | . . 3 |
7 | 2, 6 | eqeltrrd 2242 | . 2 |
8 | divalglemqt.r | . . 3 | |
9 | 8 | zcnd 9305 | . 2 |
10 | divalglemqt.s | . . 3 | |
11 | 10 | zcnd 9305 | . 2 |
12 | 2 | oveq1d 5851 | . . 3 |
13 | divalglemqt.eq | . . 3 | |
14 | 12, 13 | eqtr3d 2199 | . 2 |
15 | 7, 9, 11, 14 | addcanad 8075 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1342 wcel 2135 (class class class)co 5836 cc 7742 caddc 7747 cmul 7749 cz 9182 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 ax-setind 4508 ax-cnex 7835 ax-resscn 7836 ax-1cn 7837 ax-1re 7838 ax-icn 7839 ax-addcl 7840 ax-addrcl 7841 ax-mulcl 7842 ax-mulrcl 7843 ax-addcom 7844 ax-mulcom 7845 ax-addass 7846 ax-mulass 7847 ax-distr 7848 ax-i2m1 7849 ax-1rid 7851 ax-0id 7852 ax-rnegex 7853 ax-cnre 7855 |
This theorem depends on definitions: df-bi 116 df-3or 968 df-3an 969 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ne 2335 df-ral 2447 df-rex 2448 df-reu 2449 df-rab 2451 df-v 2723 df-sbc 2947 df-dif 3113 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-int 3819 df-br 3977 df-opab 4038 df-id 4265 df-xp 4604 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-iota 5147 df-fun 5184 df-fv 5190 df-riota 5792 df-ov 5839 df-oprab 5840 df-mpo 5841 df-sub 8062 df-neg 8063 df-inn 8849 df-n0 9106 df-z 9183 |
This theorem is referenced by: divalglemeunn 11843 divalglemeuneg 11845 |
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