Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > iseqf1olemqval | Unicode version |
Description: Lemma for seq3f1o 10308. Value of the function . (Contributed by Jim Kingdon, 28-Aug-2022.) |
Ref | Expression |
---|---|
iseqf1olemqcl.k | |
iseqf1olemqcl.j | |
iseqf1olemqcl.a | |
iseqf1olemqval.q |
Ref | Expression |
---|---|
iseqf1olemqval |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iseqf1olemqcl.a | . 2 | |
2 | iseqf1olemqcl.k | . . 3 | |
3 | iseqf1olemqcl.j | . . 3 | |
4 | 2, 3, 1 | iseqf1olemqcl 10290 | . 2 |
5 | eleq1 2203 | . . . 4 | |
6 | eqeq1 2147 | . . . . 5 | |
7 | oveq1 5789 | . . . . . 6 | |
8 | 7 | fveq2d 5433 | . . . . 5 |
9 | 6, 8 | ifbieq2d 3501 | . . . 4 |
10 | fveq2 5429 | . . . 4 | |
11 | 5, 9, 10 | ifbieq12d 3503 | . . 3 |
12 | iseqf1olemqval.q | . . 3 | |
13 | 11, 12 | fvmptg 5505 | . 2 |
14 | 1, 4, 13 | syl2anc 409 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1332 wcel 1481 cif 3479 cmpt 3997 ccnv 4546 wf1o 5130 cfv 5131 (class class class)co 5782 c1 7645 cmin 7957 cfz 9821 |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 ax-un 4363 ax-setind 4460 ax-cnex 7735 ax-resscn 7736 ax-1cn 7737 ax-1re 7738 ax-icn 7739 ax-addcl 7740 ax-addrcl 7741 ax-mulcl 7742 ax-addcom 7744 ax-addass 7746 ax-distr 7748 ax-i2m1 7749 ax-0lt1 7750 ax-0id 7752 ax-rnegex 7753 ax-cnre 7755 ax-pre-ltirr 7756 ax-pre-ltwlin 7757 ax-pre-lttrn 7758 ax-pre-ltadd 7760 |
This theorem depends on definitions: df-bi 116 df-dc 821 df-3or 964 df-3an 965 df-tru 1335 df-fal 1338 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ne 2310 df-nel 2405 df-ral 2422 df-rex 2423 df-reu 2424 df-rab 2426 df-v 2691 df-sbc 2914 df-dif 3078 df-un 3080 df-in 3082 df-ss 3089 df-if 3480 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-int 3780 df-br 3938 df-opab 3998 df-mpt 3999 df-id 4223 df-xp 4553 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-rn 4558 df-res 4559 df-ima 4560 df-iota 5096 df-fun 5133 df-fn 5134 df-f 5135 df-f1 5136 df-fo 5137 df-f1o 5138 df-fv 5139 df-riota 5738 df-ov 5785 df-oprab 5786 df-mpo 5787 df-pnf 7826 df-mnf 7827 df-xr 7828 df-ltxr 7829 df-le 7830 df-sub 7959 df-neg 7960 df-inn 8745 df-n0 9002 df-z 9079 df-uz 9351 df-fz 9822 |
This theorem is referenced by: iseqf1olemnab 10292 iseqf1olemab 10293 iseqf1olemnanb 10294 iseqf1olemqk 10298 seq3f1olemqsumkj 10302 seq3f1olemqsumk 10303 |
Copyright terms: Public domain | W3C validator |