Definition df-tpos 6312

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 6311	. 2 class tpos F
3		vx	. . . 4 setvar x
4	1	cdm 4664	. . . . . 6 class dom F
5	4	ccnv 4663	. . . . 5 class `' dom F
6		c0 3451	. . . . . 6 class (/)
7	6	csn 3623	. . . . 5 class { (/) }
8	5, 7	cun 3155	. . . 4 class ( `' dom F u. { (/) } )
9	3	cv 1363	. . . . . . 7 class x
10	9	csn 3623	. . . . . 6 class { x }
11	10	ccnv 4663	. . . . 5 class `' { x }
12	11	cuni 3840	. . . 4 class U. `' { x }
13	3, 8, 12	cmpt 4095	. . 3 class ( x e. ( `' dom F u. { (/) } ) |-> U. `' { x } )
14	1, 13	ccom 4668	. 2 class ( F o. ( x e. ( `' dom F u. { (/) } ) |-> U. `' { x } ) )
15	2, 14	wceq 1364	1 wff tpos F = ( F o. ( x e. ( `' dom F u. { (/) } ) |-> U. `' { x } ) )

This definition is referenced by:  tposss  6313  tposssxp  6316  brtpos2  6318  tposfun  6327  dftpos2  6328  dftpos4  6330