Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > riota5f | Unicode version |
Description: A method for computing restricted iota. (Contributed by NM, 16-Apr-2013.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
riota5f.1 | |
riota5f.2 | |
riota5f.3 |
Ref | Expression |
---|---|
riota5f |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | riota5f.3 | . . 3 | |
2 | 1 | ralrimiva 2392 | . 2 |
3 | riota5f.2 | . . . 4 | |
4 | a1tru 1259 | . . . . . . 7 | |
5 | reu6i 2732 | . . . . . . . . 9 | |
6 | 5 | adantl 262 | . . . . . . . 8 |
7 | nfv 1421 | . . . . . . . . . 10 | |
8 | nfv 1421 | . . . . . . . . . . 11 | |
9 | nfra1 2355 | . . . . . . . . . . 11 | |
10 | 8, 9 | nfan 1457 | . . . . . . . . . 10 |
11 | 7, 10 | nfan 1457 | . . . . . . . . 9 |
12 | nfcvd 2179 | . . . . . . . . 9 | |
13 | nfvd 1422 | . . . . . . . . 9 | |
14 | simprl 483 | . . . . . . . . 9 | |
15 | simpr 103 | . . . . . . . . . . 11 | |
16 | simplrr 488 | . . . . . . . . . . . 12 | |
17 | simplrl 487 | . . . . . . . . . . . . 13 | |
18 | 15, 17 | eqeltrd 2114 | . . . . . . . . . . . 12 |
19 | rsp 2369 | . . . . . . . . . . . 12 | |
20 | 16, 18, 19 | sylc 56 | . . . . . . . . . . 11 |
21 | 15, 20 | mpbird 156 | . . . . . . . . . 10 |
22 | a1tru 1259 | . . . . . . . . . 10 | |
23 | 21, 22 | 2thd 164 | . . . . . . . . 9 |
24 | 11, 12, 13, 14, 23 | riota2df 5488 | . . . . . . . 8 |
25 | 6, 24 | mpdan 398 | . . . . . . 7 |
26 | 4, 25 | mpbid 135 | . . . . . 6 |
27 | 26 | expr 357 | . . . . 5 |
28 | 27 | ralrimiva 2392 | . . . 4 |
29 | rspsbc 2840 | . . . 4 | |
30 | 3, 28, 29 | sylc 56 | . . 3 |
31 | nfcvd 2179 | . . . . . . . 8 | |
32 | riota5f.1 | . . . . . . . 8 | |
33 | 31, 32 | nfeqd 2192 | . . . . . . 7 |
34 | 7, 33 | nfan1 1456 | . . . . . 6 |
35 | simpr 103 | . . . . . . . 8 | |
36 | 35 | eqeq2d 2051 | . . . . . . 7 |
37 | 36 | bibi2d 221 | . . . . . 6 |
38 | 34, 37 | ralbid 2324 | . . . . 5 |
39 | 35 | eqeq2d 2051 | . . . . 5 |
40 | 38, 39 | imbi12d 223 | . . . 4 |
41 | 3, 40 | sbcied 2799 | . . 3 |
42 | 30, 41 | mpbid 135 | . 2 |
43 | 2, 42 | mpd 13 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wtru 1244 wcel 1393 wnfc 2165 wral 2306 wreu 2308 wsbc 2764 crio 5467 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-reu 2313 df-v 2559 df-sbc 2765 df-un 2922 df-sn 3381 df-pr 3382 df-uni 3581 df-iota 4867 df-riota 5468 |
This theorem is referenced by: riota5 5493 |
Copyright terms: Public domain | W3C validator |