Metamath Proof Explorer


Theorem ltsubadd2i

Description: 'Less than' relationship between subtraction and addition. (Contributed by NM, 21-Jan-1997)

Ref Expression
Hypotheses lt2.1 A
lt2.2 B
lt2.3 C
Assertion ltsubadd2i AB<CA<B+C

Proof

Step Hyp Ref Expression
1 lt2.1 A
2 lt2.2 B
3 lt2.3 C
4 ltsubadd2 ABCAB<CA<B+C
5 1 2 3 4 mp3an AB<CA<B+C