Theorem resabs2i

Description: Absorption law for restriction. (Contributed by Glauco Siliprandi, 2-Jan-2022)

	Ref	Expression
Hypothesis	resabs2i.1	|- B C_ C
Assertion	resabs2i	|- ( ( A |` B ) |` C ) = ( A |` B )

Proof

Step	Hyp	Ref	Expression
1		resabs2i.1	|- B C_ C
2		resabs2	|- ( B C_ C -> ( ( A |` B ) |` C ) = ( A |` B ) )
3	1 2	ax-mp	|- ( ( A |` B ) |` C ) = ( A |` B )