Step | Hyp | Ref
| Expression |
1 | | ctgrp 39613 |
. 2
class
TGrp |
2 | | vk |
. . 3
setvar π |
3 | | cvv 3475 |
. . 3
class
V |
4 | | vw |
. . . 4
setvar π€ |
5 | 2 | cv 1541 |
. . . . 5
class π |
6 | | clh 38855 |
. . . . 5
class
LHyp |
7 | 5, 6 | cfv 6544 |
. . . 4
class
(LHypβπ) |
8 | | cnx 17126 |
. . . . . . 7
class
ndx |
9 | | cbs 17144 |
. . . . . . 7
class
Base |
10 | 8, 9 | cfv 6544 |
. . . . . 6
class
(Baseβndx) |
11 | 4 | cv 1541 |
. . . . . . 7
class π€ |
12 | | cltrn 38972 |
. . . . . . . 8
class
LTrn |
13 | 5, 12 | cfv 6544 |
. . . . . . 7
class
(LTrnβπ) |
14 | 11, 13 | cfv 6544 |
. . . . . 6
class
((LTrnβπ)βπ€) |
15 | 10, 14 | cop 4635 |
. . . . 5
class
β¨(Baseβndx), ((LTrnβπ)βπ€)β© |
16 | | cplusg 17197 |
. . . . . . 7
class
+g |
17 | 8, 16 | cfv 6544 |
. . . . . 6
class
(+gβndx) |
18 | | vf |
. . . . . . 7
setvar π |
19 | | vg |
. . . . . . 7
setvar π |
20 | 18 | cv 1541 |
. . . . . . . 8
class π |
21 | 19 | cv 1541 |
. . . . . . . 8
class π |
22 | 20, 21 | ccom 5681 |
. . . . . . 7
class (π β π) |
23 | 18, 19, 14, 14, 22 | cmpo 7411 |
. . . . . 6
class (π β ((LTrnβπ)βπ€), π β ((LTrnβπ)βπ€) β¦ (π β π)) |
24 | 17, 23 | cop 4635 |
. . . . 5
class
β¨(+gβndx), (π β ((LTrnβπ)βπ€), π β ((LTrnβπ)βπ€) β¦ (π β π))β© |
25 | 15, 24 | cpr 4631 |
. . . 4
class
{β¨(Baseβndx), ((LTrnβπ)βπ€)β©, β¨(+gβndx),
(π β
((LTrnβπ)βπ€), π β ((LTrnβπ)βπ€) β¦ (π β π))β©} |
26 | 4, 7, 25 | cmpt 5232 |
. . 3
class (π€ β (LHypβπ) β¦
{β¨(Baseβndx), ((LTrnβπ)βπ€)β©, β¨(+gβndx),
(π β
((LTrnβπ)βπ€), π β ((LTrnβπ)βπ€) β¦ (π β π))β©}) |
27 | 2, 3, 26 | cmpt 5232 |
. 2
class (π β V β¦ (π€ β (LHypβπ) β¦
{β¨(Baseβndx), ((LTrnβπ)βπ€)β©, β¨(+gβndx),
(π β
((LTrnβπ)βπ€), π β ((LTrnβπ)βπ€) β¦ (π β π))β©})) |
28 | 1, 27 | wceq 1542 |
1
wff TGrp =
(π β V β¦ (π€ β (LHypβπ) β¦
{β¨(Baseβndx), ((LTrnβπ)βπ€)β©, β¨(+gβndx),
(π β
((LTrnβπ)βπ€), π β ((LTrnβπ)βπ€) β¦ (π β π))β©})) |