Metamath Proof Explorer


Theorem fabex

Description: Existence of a set of functions. (Contributed by NM, 3-Dec-2007)

Ref Expression
Hypotheses fabex.1 A V
fabex.2 B V
fabex.3 F = x | x : A B φ
Assertion fabex F V

Proof

Step Hyp Ref Expression
1 fabex.1 A V
2 fabex.2 B V
3 fabex.3 F = x | x : A B φ
4 3 fabexg A V B V F V
5 1 2 4 mp2an F V