Metamath Proof Explorer


Theorem lesubadd2i

Description: 'Less than or equal to' relationship between subtraction and addition. (Contributed by NM, 3-Aug-1999)

Ref Expression
Hypotheses lt2.1 A
lt2.2 B
lt2.3 C
Assertion lesubadd2i A B C A B + C

Proof

Step Hyp Ref Expression
1 lt2.1 A
2 lt2.2 B
3 lt2.3 C
4 lesubadd2 A B C A B C A B + C
5 1 2 3 4 mp3an A B C A B + C