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Mirrors > Home > ILE Home > Th. List > r19.2uz | Unicode version |
Description: A version of r19.2m 3481 for upper integer quantifiers. (Contributed by Mario Carneiro, 15-Feb-2014.) |
Ref | Expression |
---|---|
rexuz3.1 |
Ref | Expression |
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r19.2uz |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eluzelz 9453 | . . . . . 6 | |
2 | uzid 9458 | . . . . . 6 | |
3 | elex2 2728 | . . . . . 6 | |
4 | 1, 2, 3 | 3syl 17 | . . . . 5 |
5 | rexuz3.1 | . . . . 5 | |
6 | 4, 5 | eleq2s 2252 | . . . 4 |
7 | r19.2m 3481 | . . . 4 | |
8 | 6, 7 | sylan 281 | . . 3 |
9 | 5 | uztrn2 9461 | . . . . . . 7 |
10 | 9 | ex 114 | . . . . . 6 |
11 | 10 | anim1d 334 | . . . . 5 |
12 | 11 | reximdv2 2556 | . . . 4 |
13 | 12 | imp 123 | . . 3 |
14 | 8, 13 | syldan 280 | . 2 |
15 | 14 | rexlimiva 2569 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1335 wex 1472 wcel 2128 wral 2435 wrex 2436 cfv 5172 cz 9172 cuz 9444 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-13 2130 ax-14 2131 ax-ext 2139 ax-sep 4084 ax-pow 4137 ax-pr 4171 ax-un 4395 ax-setind 4498 ax-cnex 7825 ax-resscn 7826 ax-pre-ltirr 7846 ax-pre-ltwlin 7847 |
This theorem depends on definitions: df-bi 116 df-3or 964 df-3an 965 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ne 2328 df-nel 2423 df-ral 2440 df-rex 2441 df-rab 2444 df-v 2714 df-sbc 2938 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-br 3968 df-opab 4028 df-mpt 4029 df-id 4255 df-xp 4594 df-rel 4595 df-cnv 4596 df-co 4597 df-dm 4598 df-rn 4599 df-res 4600 df-ima 4601 df-iota 5137 df-fun 5174 df-fn 5175 df-f 5176 df-fv 5180 df-ov 5829 df-pnf 7916 df-mnf 7917 df-xr 7918 df-ltxr 7919 df-le 7920 df-neg 8053 df-z 9173 df-uz 9445 |
This theorem is referenced by: recvguniq 10906 climge0 11233 |
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