Definition df-cda 8990

Description: Define cardinal number addition. Definition of cardinal sum in [Mendelson] p. 258. See cdaval 8992 for its value and a description. (Contributed by NM, 24-Sep-2004.)

Assertion

Ref	Expression
df-cda	|- +c = ( x e. _V , y e. _V |-> ( ( x X. { (/) } ) u. ( y X. { 1o } ) ) )

Distinct variable group:   x, y

Detailed syntax breakdown of Definition df-cda

Step	Hyp	Ref	Expression
1		ccda 8989	. 2 class +c
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4		cvv 3200	. . 3 class _V
5	2	cv 1482	. . . . 5 class x
6		c0 3915	. . . . . 6 class (/)
7	6	csn 4177	. . . . 5 class { (/) }
8	5, 7	cxp 5112	. . . 4 class ( x X. { (/) } )
9	3	cv 1482	. . . . 5 class y
10		c1o 7553	. . . . . 6 class 1o
11	10	csn 4177	. . . . 5 class { 1o }
12	9, 11	cxp 5112	. . . 4 class ( y X. { 1o } )
13	8, 12	cun 3572	. . 3 class ( ( x X. { (/) } ) u. ( y X. { 1o } ) )
14	2, 3, 4, 4, 13	cmpt2 6652	. 2 class ( x e. _V , y e. _V |-> ( ( x X. { (/) } ) u. ( y X. { 1o } ) ) )
15	1, 14	wceq 1483	1 wff +c = ( x e. _V , y e. _V |-> ( ( x X. { (/) } ) u. ( y X. { 1o } ) ) )

This definition is referenced by:  cdafn  8991  cdaval  8992