Metamath Proof Explorer


Theorem logne0d

Description: Deduction form of logne0 . See logccne0d for a more general version. (Contributed by SN, 25-Apr-2025)

Ref Expression
Hypotheses logne0d.a φ A +
logne0d.1 φ A 1
Assertion logne0d φ log A 0

Proof

Step Hyp Ref Expression
1 logne0d.a φ A +
2 logne0d.1 φ A 1
3 logne0 A + A 1 log A 0
4 1 2 3 syl2anc φ log A 0