Theorem resabs1i

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

	Ref	Expression
Hypothesis	resabs1i.1	|- B C_ C
Assertion	resabs1i	|- ( ( A |` C ) |` B ) = ( A |` B )

Proof

Step	Hyp	Ref	Expression
1		resabs1i.1	|- B C_ C
2		resabs1	|- ( B C_ C -> ( ( A |` C ) |` B ) = ( A |` B ) )
3	1 2	ax-mp	|- ( ( A |` C ) |` B ) = ( A |` B )