Metamath Proof Explorer


Theorem nmull0d

Description: Natural multiplication by zero. Deduction form. (Contributed by Scott Fenton, 30-Jul-2026)

Ref Expression
Hypothesis nmul.1 φ A On
Assertion nmull0d Could not format assertion : No typesetting found for |- ( ph -> ( (/) .no A ) = (/) ) with typecode |-

Proof

Step Hyp Ref Expression
1 nmul.1 φ A On
2 nmull0 Could not format ( A e. On -> ( (/) .no A ) = (/) ) : No typesetting found for |- ( A e. On -> ( (/) .no A ) = (/) ) with typecode |-
3 1 2 syl Could not format ( ph -> ( (/) .no A ) = (/) ) : No typesetting found for |- ( ph -> ( (/) .no A ) = (/) ) with typecode |-