Description: Value of vector subtraction in terms of addition. ( hvsubval analog.) (Contributed by NM, 31-Mar-2014) (Proof shortened by Mario Carneiro, 19-Jun-2014)
Ref | Expression | ||
---|---|---|---|
Hypotheses | lmodvsubval2.v | |
|
lmodvsubval2.p | |
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lmodvsubval2.m | |
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lmodvsubval2.f | |
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lmodvsubval2.s | |
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lmodvsubval2.n | |
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lmodvsubval2.u | |
||
Assertion | lmodvsubval2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lmodvsubval2.v | |
|
2 | lmodvsubval2.p | |
|
3 | lmodvsubval2.m | |
|
4 | lmodvsubval2.f | |
|
5 | lmodvsubval2.s | |
|
6 | lmodvsubval2.n | |
|
7 | lmodvsubval2.u | |
|
8 | eqid | |
|
9 | 1 2 8 3 | grpsubval | |
10 | 9 | 3adant1 | |
11 | 1 8 4 5 7 6 | lmodvneg1 | |
12 | 11 | 3adant2 | |
13 | 12 | oveq2d | |
14 | 10 13 | eqtr4d | |