Theorem resabs1d

Description: Absorption law for restriction, deduction form. (Contributed by Glauco Siliprandi, 11-Dec-2019)

	Ref	Expression
Hypothesis	resabs1d.b	|- ( ph -> B C_ C )
Assertion	resabs1d	|- ( ph -> ( ( A |` C ) |` B ) = ( A |` B ) )

Proof

Step	Hyp	Ref	Expression
1		resabs1d.b	|- ( ph -> B C_ C )
2		resabs1	|- ( B C_ C -> ( ( A |` C ) |` B ) = ( A |` B ) )
3	1 2	syl	|- ( ph -> ( ( A |` C ) |` B ) = ( A |` B ) )