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Mirrors > Home > MPE Home > Th. List > chrval | Structured version Visualization version Unicode version |
Description: Definition substitution of the ring characteristic. (Contributed by Stefan O'Rear, 5-Sep-2015.) |
Ref | Expression |
---|---|
chrval.o | |
chrval.u | |
chrval.c | chr |
Ref | Expression |
---|---|
chrval |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | chrval.c | . 2 chr | |
2 | fveq2 6191 | . . . . . 6 | |
3 | chrval.o | . . . . . 6 | |
4 | 2, 3 | syl6eqr 2674 | . . . . 5 |
5 | fveq2 6191 | . . . . . 6 | |
6 | chrval.u | . . . . . 6 | |
7 | 5, 6 | syl6eqr 2674 | . . . . 5 |
8 | 4, 7 | fveq12d 6197 | . . . 4 |
9 | df-chr 19854 | . . . 4 chr | |
10 | fvex 6201 | . . . 4 | |
11 | 8, 9, 10 | fvmpt 6282 | . . 3 chr |
12 | fvprc 6185 | . . . 4 chr | |
13 | fvprc 6185 | . . . . . . 7 | |
14 | 3, 13 | syl5eq 2668 | . . . . . 6 |
15 | 14 | fveq1d 6193 | . . . . 5 |
16 | 0fv 6227 | . . . . 5 | |
17 | 15, 16 | syl6eq 2672 | . . . 4 |
18 | 12, 17 | eqtr4d 2659 | . . 3 chr |
19 | 11, 18 | pm2.61i 176 | . 2 chr |
20 | 1, 19 | eqtr2i 2645 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wceq 1483 wcel 1990 cvv 3200 c0 3915 cfv 5888 cod 17944 cur 18501 chrcchr 19850 |
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-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 |
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-mo 2475 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-sbc 3436 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-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-iota 5851 df-fun 5890 df-fv 5896 df-chr 19854 |
This theorem is referenced by: chrcl 19874 chrid 19875 chrdvds 19876 chrcong 19877 subrgchr 29794 ofldchr 29814 zrhchr 30020 |
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