Theorem resabs2d

Description: Absorption law for restriction. (Contributed by Glauco Siliprandi, 23-Oct-2021)

	Ref	Expression
Hypothesis	resabs2d.1	|- ( ph -> B C_ C )
Assertion	resabs2d	|- ( ph -> ( ( A |` B ) |` C ) = ( A |` B ) )

Proof

Step	Hyp	Ref	Expression
1		resabs2d.1	|- ( ph -> B C_ C )
2		resabs2	|- ( B C_ C -> ( ( A |` B ) |` C ) = ( A |` B ) )
3	1 2	syl	|- ( ph -> ( ( A |` B ) |` C ) = ( A |` B ) )