Metamath Proof Explorer


Definition df-shs

Description: Define subspace sum in SH . See shsval , shsval2i , and shsval3i for its value. (Contributed by NM, 16-Oct-1999) (New usage is discouraged.)

Ref Expression
Assertion df-shs
|- +H = ( x e. SH , y e. SH |-> ( +h " ( x X. y ) ) )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cph
 |-  +H
1 vx
 |-  x
2 csh
 |-  SH
3 vy
 |-  y
4 cva
 |-  +h
5 1 cv
 |-  x
6 3 cv
 |-  y
7 5 6 cxp
 |-  ( x X. y )
8 4 7 cima
 |-  ( +h " ( x X. y ) )
9 1 3 2 2 8 cmpo
 |-  ( x e. SH , y e. SH |-> ( +h " ( x X. y ) ) )
10 0 9 wceq
 |-  +H = ( x e. SH , y e. SH |-> ( +h " ( x X. y ) ) )