Metamath Proof Explorer


Theorem subge0d

Description: Nonnegative subtraction. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses leidd.1 φA
ltnegd.2 φB
Assertion subge0d φ0ABBA

Proof

Step Hyp Ref Expression
1 leidd.1 φA
2 ltnegd.2 φB
3 subge0 AB0ABBA
4 1 2 3 syl2anc φ0ABBA