Metamath Proof Explorer


Theorem nmullidd

Description: Identity law for natural multiplication. Deduction form. (Contributed by Scott Fenton, 30-Jul-2026)

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

Proof

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