Definition df-tpos 5801

Description: Define the transposition of a function, which is a function G = tpos F satisfying G(x , y) = F(y , x). (Contributed by Mario Carneiro, 10-Sep-2015.)

Assertion

Ref	Expression
df-tpos	|- tpos F = ( F o. (x e. ( `' dom F u. { (/) }) |-> U. `' {x }))

Distinct variable group:   x, F

Detailed syntax breakdown of Definition df-tpos

Step	Hyp	Ref	Expression
1		cF	. . 3 class F
2	1	ctpos 5800	. 2 class tpos F
3		vx	. . . 4 setvar x
4	1	cdm 4288	. . . . . 6 class dom F
5	4	ccnv 4287	. . . . 5 class `' dom F
6		c0 3218	. . . . . 6 class (/)
7	6	csn 3367	. . . . 5 class { (/) }
8	5, 7	cun 2909	. . . 4 class ( `' dom F u. { (/) })
9	3	cv 1241	. . . . . . 7 class x
10	9	csn 3367	. . . . . 6 class {x }
11	10	ccnv 4287	. . . . 5 class `' {x }
12	11	cuni 3571	. . . 4 class U. `' {x }
13	3, 8, 12	cmpt 3809	. . 3 class (x e. ( `' dom F u. { (/) }) |-> U. `' {x })
14	1, 13	ccom 4292	. 2 class ( F o. (x e. ( `' dom F u. { (/) }) |-> U. `' {x }))
15	2, 14	wceq 1242	1 wff tpos F = ( F o. (x e. ( `' dom F u. { (/) }) |-> U. `' {x }))

This definition is referenced by:  tposss  5802  tposssxp  5805  brtpos2  5807  tposfun  5816  dftpos2  5817  dftpos4  5819