Definition df-xneg 10666

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 10663	. 2 class - e A
3		cpnf 9073	. . . 4 class +oo
4	1, 3	wceq 1649	. . 3 wff A = +oo
5		cmnf 9074	. . 3 class -oo
6	1, 5	wceq 1649	. . . 4 wff A = -oo
7	1	cneg 9248	. . . 4 class -u A
8	6, 3, 7	cif 3699	. . 3 class if ( A = -oo , +oo , -u A )
9	4, 5, 8	cif 3699	. 2 class if ( A = +oo , -oo , if ( A = -oo , +oo , -u A ) )
10	2, 9	wceq 1649	1 wff - e A = if ( A = +oo , -oo , if ( A = -oo , +oo , -u A ) )

This definition is referenced by:  xnegeq  10749  xnegex  10750  xnegpnf  10751  xnegmnf  10752  rexneg  10753