Metamath Proof Explorer

Theorem resabs2

Description: Absorption law for restriction. (Contributed by NM, 27-Mar-1998)

Ref Expression
Assertion resabs2 
|- ( B C_ C -> ( ( A |` B ) |` C ) = ( A |` B ) )

Proof

Step Hyp Ref Expression
1 rescom 
 |-  ( ( A |` B ) |` C ) = ( ( A |` C ) |` B )
2 resabs1 
 |-  ( B C_ C -> ( ( A |` C ) |` B ) = ( A |` B ) )
3 1 2 eqtrid 
 |-  ( B C_ C -> ( ( A |` B ) |` C ) = ( A |` B ) )