Metamath Proof Explorer


Theorem funres

Description: A restriction of a function is a function. Compare Exercise 18 of TakeutiZaring p. 25. (Contributed by NM, 16-Aug-1994)

Ref Expression
Assertion funres FunFFunFA

Proof

Step Hyp Ref Expression
1 resss FAF
2 funss FAFFunFFunFA
3 1 2 ax-mp FunFFunFA