Definition df-xneg 9708

Description: Define the negative of an extended real number. (Contributed by FL, 26-Dec-2011.)

Assertion

Ref	Expression
df-xneg	|- -e A = if ( A = +oo , -oo , if ( A = -oo , +oo , -u A ) )

Detailed syntax breakdown of Definition df-xneg

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2	1	cxne 9705	. 2 class -e A
3		cpnf 7930	. . . 4 class +oo
4	1, 3	wceq 1343	. . 3 wff A = +oo
5		cmnf 7931	. . 3 class -oo
6	1, 5	wceq 1343	. . . 4 wff A = -oo
7	1	cneg 8070	. . . 4 class -u A
8	6, 3, 7	cif 3520	. . 3 class if ( A = -oo , +oo , -u A )
9	4, 5, 8	cif 3520	. 2 class if ( A = +oo , -oo , if ( A = -oo , +oo , -u A ) )
10	2, 9	wceq 1343	1 wff -e A = if ( A = +oo , -oo , if ( A = -oo , +oo , -u A ) )

This definition is referenced by:  xnegeq  9763  xnegpnf  9764  xnegmnf  9765  rexneg  9766