Metamath Proof Explorer


Theorem subcld

Description: Closure law for subtraction. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses negidd.1 φ A
pncand.2 φ B
Assertion subcld φ A B

Proof

Step Hyp Ref Expression
1 negidd.1 φ A
2 pncand.2 φ B
3 subcl A B A B
4 1 2 3 syl2anc φ A B