Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > riota5f | Structured version Visualization version 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 2966 | . 2 |
3 | riota5f.2 | . . . 4 | |
4 | a1tru 1500 | . . . . . . 7 | |
5 | reu6i 3397 | . . . . . . . . 9 | |
6 | 5 | adantl 482 | . . . . . . . 8 |
7 | nfv 1843 | . . . . . . . . . 10 | |
8 | nfv 1843 | . . . . . . . . . . 11 | |
9 | nfra1 2941 | . . . . . . . . . . 11 | |
10 | 8, 9 | nfan 1828 | . . . . . . . . . 10 |
11 | 7, 10 | nfan 1828 | . . . . . . . . 9 |
12 | nfcvd 2765 | . . . . . . . . 9 | |
13 | nfvd 1844 | . . . . . . . . 9 | |
14 | simprl 794 | . . . . . . . . 9 | |
15 | simpr 477 | . . . . . . . . . . 11 | |
16 | simplrr 801 | . . . . . . . . . . . 12 | |
17 | simplrl 800 | . . . . . . . . . . . . 13 | |
18 | 15, 17 | eqeltrd 2701 | . . . . . . . . . . . 12 |
19 | rsp 2929 | . . . . . . . . . . . 12 | |
20 | 16, 18, 19 | sylc 65 | . . . . . . . . . . 11 |
21 | 15, 20 | mpbird 247 | . . . . . . . . . 10 |
22 | a1tru 1500 | . . . . . . . . . 10 | |
23 | 21, 22 | 2thd 255 | . . . . . . . . 9 |
24 | 11, 12, 13, 14, 23 | riota2df 6631 | . . . . . . . 8 |
25 | 6, 24 | mpdan 702 | . . . . . . 7 |
26 | 4, 25 | mpbid 222 | . . . . . 6 |
27 | 26 | expr 643 | . . . . 5 |
28 | 27 | ralrimiva 2966 | . . . 4 |
29 | rspsbc 3518 | . . . 4 | |
30 | 3, 28, 29 | sylc 65 | . . 3 |
31 | nfcvd 2765 | . . . . . . . 8 | |
32 | riota5f.1 | . . . . . . . 8 | |
33 | 31, 32 | nfeqd 2772 | . . . . . . 7 |
34 | 7, 33 | nfan1 2068 | . . . . . 6 |
35 | simpr 477 | . . . . . . . 8 | |
36 | 35 | eqeq2d 2632 | . . . . . . 7 |
37 | 36 | bibi2d 332 | . . . . . 6 |
38 | 34, 37 | ralbid 2983 | . . . . 5 |
39 | 35 | eqeq2d 2632 | . . . . 5 |
40 | 38, 39 | imbi12d 334 | . . . 4 |
41 | 3, 40 | sbcied 3472 | . . 3 |
42 | 30, 41 | mpbid 222 | . 2 |
43 | 2, 42 | mpd 15 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wtru 1484 wcel 1990 wnfc 2751 wral 2912 wreu 2914 wsbc 3435 crio 6610 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-reu 2919 df-v 3202 df-sbc 3436 df-un 3579 df-sn 4178 df-pr 4180 df-uni 4437 df-iota 5851 df-riota 6611 |
This theorem is referenced by: riota5 6637 |
Copyright terms: Public domain | W3C validator |