Metamath Proof Explorer


Theorem nmulridd

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

Ref Expression
Hypothesis nmul.1 ( 𝜑𝐴 ∈ On )
Assertion nmulridd ( 𝜑 → ( 𝐴 ·no 1o ) = 𝐴 )

Proof

Step Hyp Ref Expression
1 nmul.1 ( 𝜑𝐴 ∈ On )
2 nmulrid ( 𝐴 ∈ On → ( 𝐴 ·no 1o ) = 𝐴 )
3 1 2 syl ( 𝜑 → ( 𝐴 ·no 1o ) = 𝐴 )