Description: Move intersection into class restriction. (Contributed by NM, 18-Dec-2008)
Ref | Expression | ||
---|---|---|---|
Assertion | inres | |- ( A i^i ( B |` C ) ) = ( ( A i^i B ) |` C ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inass | |- ( ( A i^i B ) i^i ( C X. _V ) ) = ( A i^i ( B i^i ( C X. _V ) ) ) |
|
2 | df-res | |- ( ( A i^i B ) |` C ) = ( ( A i^i B ) i^i ( C X. _V ) ) |
|
3 | df-res | |- ( B |` C ) = ( B i^i ( C X. _V ) ) |
|
4 | 3 | ineq2i | |- ( A i^i ( B |` C ) ) = ( A i^i ( B i^i ( C X. _V ) ) ) |
5 | 1 2 4 | 3eqtr4ri | |- ( A i^i ( B |` C ) ) = ( ( A i^i B ) |` C ) |