Theorem fnpm

Description: Partial function exponentiation has a universal domain. (Contributed by Mario Carneiro, 14-Nov-2013)

	Ref	Expression
Assertion	fnpm	|- ^pm Fn ( _V X. _V )

Proof

Step	Hyp	Ref	Expression
1		df-pm	|- ^pm = ( x e. _V , y e. _V |-> { f e. ~P ( y X. x ) | Fun f } )
2		vex	|- y e. _V
3		vex	|- x e. _V
4	2 3	xpex	|- ( y X. x ) e. _V
5	4	pwex	|- ~P ( y X. x ) e. _V
6	5	rabex	|- { f e. ~P ( y X. x ) | Fun f } e. _V
7	1 6	fnmpoi	|- ^pm Fn ( _V X. _V )