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Mirrors > Home > ILE Home > Th. List > fzass4 | Unicode version |
Description: Two ways to express a nondecreasing sequence of four integers. (Contributed by Stefan O'Rear, 15-Aug-2015.) |
Ref | Expression |
---|---|
fzass4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpll 519 | . . . . 5 | |
2 | simprl 521 | . . . . 5 | |
3 | 1, 2 | jca 304 | . . . 4 |
4 | uztrn 9474 | . . . . . 6 | |
5 | 4 | ancoms 266 | . . . . 5 |
6 | 5 | ad2ant2r 501 | . . . 4 |
7 | simprr 522 | . . . 4 | |
8 | 3, 6, 7 | jca32 308 | . . 3 |
9 | simpll 519 | . . . . 5 | |
10 | uztrn 9474 | . . . . . . 7 | |
11 | 10 | ancoms 266 | . . . . . 6 |
12 | 11 | ad2ant2l 500 | . . . . 5 |
13 | 9, 12 | jca 304 | . . . 4 |
14 | simplr 520 | . . . 4 | |
15 | simprr 522 | . . . 4 | |
16 | 13, 14, 15 | jca32 308 | . . 3 |
17 | 8, 16 | impbii 125 | . 2 |
18 | elfzuzb 9946 | . . 3 | |
19 | elfzuzb 9946 | . . 3 | |
20 | 18, 19 | anbi12i 456 | . 2 |
21 | elfzuzb 9946 | . . 3 | |
22 | elfzuzb 9946 | . . 3 | |
23 | 21, 22 | anbi12i 456 | . 2 |
24 | 17, 20, 23 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wcel 2135 cfv 5183 (class class class)co 5837 cuz 9458 cfz 9936 |
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-13 2137 ax-14 2138 ax-ext 2146 ax-sep 4095 ax-pow 4148 ax-pr 4182 ax-un 4406 ax-setind 4509 ax-cnex 7836 ax-resscn 7837 ax-pre-ltwlin 7858 |
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-nel 2430 df-ral 2447 df-rex 2448 df-rab 2451 df-v 2724 df-sbc 2948 df-dif 3114 df-un 3116 df-in 3118 df-ss 3125 df-pw 3556 df-sn 3577 df-pr 3578 df-op 3580 df-uni 3785 df-br 3978 df-opab 4039 df-mpt 4040 df-id 4266 df-xp 4605 df-rel 4606 df-cnv 4607 df-co 4608 df-dm 4609 df-rn 4610 df-res 4611 df-ima 4612 df-iota 5148 df-fun 5185 df-fn 5186 df-f 5187 df-fv 5191 df-ov 5840 df-oprab 5841 df-mpo 5842 df-pnf 7927 df-mnf 7928 df-xr 7929 df-ltxr 7930 df-le 7931 df-neg 8064 df-z 9184 df-uz 9459 df-fz 9937 |
This theorem is referenced by: (None) |
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