Theorem resmptd

Description: Restriction of the mapping operation, deduction form. (Contributed by Glauco Siliprandi, 11-Dec-2019)

	Ref	Expression
Hypothesis	resmptd.b	|- ( ph -> B C_ A )
Assertion	resmptd	|- ( ph -> ( ( x e. A |-> C ) |` B ) = ( x e. B |-> C ) )

Proof

Step	Hyp	Ref	Expression
1		resmptd.b	|- ( ph -> B C_ A )
2		resmpt	|- ( B C_ A -> ( ( x e. A |-> C ) |` B ) = ( x e. B |-> C ) )
3	1 2	syl	|- ( ph -> ( ( x e. A |-> C ) |` B ) = ( x e. B |-> C ) )