Metamath Proof Explorer


Theorem sn-redividd

Description: A number divided by itself is 1. (Contributed by SN, 2-Apr-2026)

Ref Expression
Hypotheses sn-rediv0d.a φ A
sn-rediv0d.z φ A 0
Assertion sn-redividd Could not format assertion : No typesetting found for |- ( ph -> ( A /R A ) = 1 ) with typecode |-

Proof

Step Hyp Ref Expression
1 sn-rediv0d.a φ A
2 sn-rediv0d.z φ A 0
3 eqidd φ A = A
4 1 1 2 rediveq1d Could not format ( ph -> ( ( A /R A ) = 1 <-> A = A ) ) : No typesetting found for |- ( ph -> ( ( A /R A ) = 1 <-> A = A ) ) with typecode |-
5 3 4 mpbird Could not format ( ph -> ( A /R A ) = 1 ) : No typesetting found for |- ( ph -> ( A /R A ) = 1 ) with typecode |-