Metamath Proof Explorer


Theorem fun2ssres

Description: Equality of restrictions of a function and a subclass. (Contributed by NM, 16-Aug-1994)

Ref Expression
Assertion fun2ssres FunFGFAdomGFA=GA

Proof

Step Hyp Ref Expression
1 resabs1 AdomGFdomGA=FA
2 1 eqcomd AdomGFA=FdomGA
3 funssres FunFGFFdomG=G
4 3 reseq1d FunFGFFdomGA=GA
5 2 4 sylan9eqr FunFGFAdomGFA=GA
6 5 3impa FunFGFAdomGFA=GA