Metamath Proof Explorer


Theorem sgrp2nmnd

Description: A small semigroup (with two elements) which is not a monoid. (Contributed by AV, 26-Jan-2020)

Ref Expression
Hypotheses mgm2nsgrp.s S = A B
mgm2nsgrp.b Base M = S
sgrp2nmnd.o + M = x S , y S if x = A A B
Assertion sgrp2nmnd Could not format assertion : No typesetting found for |- ( ( # ` S ) = 2 -> ( M e. Smgrp /\ M e/ Mnd ) ) with typecode |-

Proof

Step Hyp Ref Expression
1 mgm2nsgrp.s S = A B
2 mgm2nsgrp.b Base M = S
3 sgrp2nmnd.o + M = x S , y S if x = A A B
4 1 2 3 sgrp2nmndlem4 Could not format ( ( # ` S ) = 2 -> M e. Smgrp ) : No typesetting found for |- ( ( # ` S ) = 2 -> M e. Smgrp ) with typecode |-
5 1 2 3 sgrp2nmndlem5 S = 2 M Mnd
6 4 5 jca Could not format ( ( # ` S ) = 2 -> ( M e. Smgrp /\ M e/ Mnd ) ) : No typesetting found for |- ( ( # ` S ) = 2 -> ( M e. Smgrp /\ M e/ Mnd ) ) with typecode |-