Metamath Proof Explorer


Theorem hvsubassi

Description: Hilbert vector space associative law for subtraction. (Contributed by NM, 7-Oct-1999) (Revised by Mario Carneiro, 15-May-2014) (New usage is discouraged.)

Ref Expression
Hypotheses hvass.1 A
hvass.2 B
hvass.3 C
Assertion hvsubassi A - B - C = A - B + C

Proof

Step Hyp Ref Expression
1 hvass.1 A
2 hvass.2 B
3 hvass.3 C
4 hvsubass A B C A - B - C = A - B + C
5 1 2 3 4 mp3an A - B - C = A - B + C