Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > djhfval | Structured version Visualization version Unicode version |
Description: Subspace join for vector space. (Contributed by NM, 19-Jul-2014.) |
Ref | Expression |
---|---|
djhval.h | |
djhval.u | |
djhval.v | |
djhval.o | |
djhval.j | joinH |
Ref | Expression |
---|---|
djhfval |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | djhval.j | . . 3 joinH | |
2 | djhval.h | . . . . 5 | |
3 | 2 | djhffval 36685 | . . . 4 joinH |
4 | 3 | fveq1d 6193 | . . 3 joinH |
5 | 1, 4 | syl5eq 2668 | . 2 |
6 | fveq2 6191 | . . . . . . 7 | |
7 | 6 | fveq2d 6195 | . . . . . 6 |
8 | djhval.v | . . . . . . 7 | |
9 | djhval.u | . . . . . . . 8 | |
10 | 9 | fveq2i 6194 | . . . . . . 7 |
11 | 8, 10 | eqtri 2644 | . . . . . 6 |
12 | 7, 11 | syl6eqr 2674 | . . . . 5 |
13 | 12 | pweqd 4163 | . . . 4 |
14 | fveq2 6191 | . . . . . 6 | |
15 | djhval.o | . . . . . 6 | |
16 | 14, 15 | syl6eqr 2674 | . . . . 5 |
17 | 16 | fveq1d 6193 | . . . . . 6 |
18 | 16 | fveq1d 6193 | . . . . . 6 |
19 | 17, 18 | ineq12d 3815 | . . . . 5 |
20 | 16, 19 | fveq12d 6197 | . . . 4 |
21 | 13, 13, 20 | mpt2eq123dv 6717 | . . 3 |
22 | eqid 2622 | . . 3 | |
23 | fvex 6201 | . . . . . 6 | |
24 | 8, 23 | eqeltri 2697 | . . . . 5 |
25 | 24 | pwex 4848 | . . . 4 |
26 | 25, 25 | mpt2ex 7247 | . . 3 |
27 | 21, 22, 26 | fvmpt 6282 | . 2 |
28 | 5, 27 | sylan9eq 2676 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 cvv 3200 cin 3573 cpw 4158 cmpt 4729 cfv 5888 cmpt2 6652 cbs 15857 clh 35270 cdvh 36367 coch 36636 joinHcdjh 36683 |
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-rep 4771 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-un 6949 |
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-ne 2795 df-ral 2917 df-rex 2918 df-reu 2919 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-iun 4522 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-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-oprab 6654 df-mpt2 6655 df-1st 7168 df-2nd 7169 df-djh 36684 |
This theorem is referenced by: djhval 36687 |
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