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Mirrors > Home > MPE Home > Th. List > mdetunilem4 | Structured version Visualization version Unicode version |
Description: Lemma for mdetuni 20428. (Contributed by SO, 15-Jul-2018.) |
Ref | Expression |
---|---|
mdetuni.a | Mat |
mdetuni.b | |
mdetuni.k | |
mdetuni.0g | |
mdetuni.1r | |
mdetuni.pg | |
mdetuni.tg | |
mdetuni.n | |
mdetuni.r | |
mdetuni.ff | |
mdetuni.al | |
mdetuni.li | |
mdetuni.sc |
Ref | Expression |
---|---|
mdetunilem4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp32 1098 | . 2 | |
2 | simp33 1099 | . 2 | |
3 | simp1 1061 | . . 3 | |
4 | simp23 1096 | . . . 4 | |
5 | simp3 1063 | . . . 4 | |
6 | simp21 1094 | . . . . 5 | |
7 | simp22 1095 | . . . . 5 | |
8 | mdetuni.sc | . . . . . 6 | |
9 | 8 | 3ad2ant1 1082 | . . . . 5 |
10 | reseq1 5390 | . . . . . . . . . 10 | |
11 | 10 | eqeq1d 2624 | . . . . . . . . 9 |
12 | reseq1 5390 | . . . . . . . . . 10 | |
13 | 12 | eqeq1d 2624 | . . . . . . . . 9 |
14 | 11, 13 | anbi12d 747 | . . . . . . . 8 |
15 | fveq2 6191 | . . . . . . . . 9 | |
16 | 15 | eqeq1d 2624 | . . . . . . . 8 |
17 | 14, 16 | imbi12d 334 | . . . . . . 7 |
18 | 17 | 2ralbidv 2989 | . . . . . 6 |
19 | sneq 4187 | . . . . . . . . . . . 12 | |
20 | 19 | xpeq2d 5139 | . . . . . . . . . . 11 |
21 | 20 | oveq1d 6665 | . . . . . . . . . 10 |
22 | 21 | eqeq2d 2632 | . . . . . . . . 9 |
23 | 22 | anbi1d 741 | . . . . . . . 8 |
24 | oveq1 6657 | . . . . . . . . 9 | |
25 | 24 | eqeq2d 2632 | . . . . . . . 8 |
26 | 23, 25 | imbi12d 334 | . . . . . . 7 |
27 | 26 | 2ralbidv 2989 | . . . . . 6 |
28 | 18, 27 | rspc2va 3323 | . . . . 5 |
29 | 6, 7, 9, 28 | syl21anc 1325 | . . . 4 |
30 | reseq1 5390 | . . . . . . . . 9 | |
31 | 30 | oveq2d 6666 | . . . . . . . 8 |
32 | 31 | eqeq2d 2632 | . . . . . . 7 |
33 | reseq1 5390 | . . . . . . . 8 | |
34 | 33 | eqeq2d 2632 | . . . . . . 7 |
35 | 32, 34 | anbi12d 747 | . . . . . 6 |
36 | fveq2 6191 | . . . . . . . 8 | |
37 | 36 | oveq2d 6666 | . . . . . . 7 |
38 | 37 | eqeq2d 2632 | . . . . . 6 |
39 | 35, 38 | imbi12d 334 | . . . . 5 |
40 | sneq 4187 | . . . . . . . . . 10 | |
41 | 40 | xpeq1d 5138 | . . . . . . . . 9 |
42 | 41 | reseq2d 5396 | . . . . . . . 8 |
43 | 41 | xpeq1d 5138 | . . . . . . . . 9 |
44 | 41 | reseq2d 5396 | . . . . . . . . 9 |
45 | 43, 44 | oveq12d 6668 | . . . . . . . 8 |
46 | 42, 45 | eqeq12d 2637 | . . . . . . 7 |
47 | 40 | difeq2d 3728 | . . . . . . . . . 10 |
48 | 47 | xpeq1d 5138 | . . . . . . . . 9 |
49 | 48 | reseq2d 5396 | . . . . . . . 8 |
50 | 48 | reseq2d 5396 | . . . . . . . 8 |
51 | 49, 50 | eqeq12d 2637 | . . . . . . 7 |
52 | 46, 51 | anbi12d 747 | . . . . . 6 |
53 | 52 | imbi1d 331 | . . . . 5 |
54 | 39, 53 | rspc2va 3323 | . . . 4 |
55 | 4, 5, 29, 54 | syl21anc 1325 | . . 3 |
56 | 3, 55 | syl3an3 1361 | . 2 |
57 | 1, 2, 56 | mp2and 715 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 w3a 1037 wceq 1483 wcel 1990 wne 2794 wral 2912 cdif 3571 csn 4177 cxp 5112 cres 5116 wf 5884 cfv 5888 (class class class)co 6650 cof 6895 cfn 7955 cbs 15857 cplusg 15941 cmulr 15942 c0g 16100 cur 18501 crg 18547 Mat cmat 20213 |
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-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-xp 5120 df-res 5126 df-iota 5851 df-fv 5896 df-ov 6653 |
This theorem is referenced by: mdetuni0 20427 |
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