Theorem isnmgm

Description: A condition for a structure not to be a magma. (Contributed by AV, 30-Jan-2020) (Proof shortened by NM, 5-Feb-2020)

	Ref	Expression
Hypotheses	mgmcl.b	$$⊢B={\mathrm{Base}}_M$$
	mgmcl.o	No typesetting found for |- .o. = ( +g ` M ) with typecode |-
Assertion	isnmgm	Could not format assertion : No typesetting found for |- ( ( X e. B /\ Y e. B /\ ( X .o. Y ) e/ B ) -> M e/ Mgm ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		mgmcl.b	$$⊢B={\mathrm{Base}}_M$$
2		mgmcl.o	Could not format .o. = ( +g ` M ) : No typesetting found for |- .o. = ( +g ` M ) with typecode |-
3	1 2	mgmcl	Could not format ( ( M e. Mgm /\ X e. B /\ Y e. B ) -> ( X .o. Y ) e. B ) : No typesetting found for |- ( ( M e. Mgm /\ X e. B /\ Y e. B ) -> ( X .o. Y ) e. B ) with typecode |-
4	3	3expib	Could not format ( M e. Mgm -> ( ( X e. B /\ Y e. B ) -> ( X .o. Y ) e. B ) ) : No typesetting found for |- ( M e. Mgm -> ( ( X e. B /\ Y e. B ) -> ( X .o. Y ) e. B ) ) with typecode |-
5	4	com12	Could not format ( ( X e. B /\ Y e. B ) -> ( M e. Mgm -> ( X .o. Y ) e. B ) ) : No typesetting found for |- ( ( X e. B /\ Y e. B ) -> ( M e. Mgm -> ( X .o. Y ) e. B ) ) with typecode |-
6	5	nelcon3d	Could not format ( ( X e. B /\ Y e. B ) -> ( ( X .o. Y ) e/ B -> M e/ Mgm ) ) : No typesetting found for |- ( ( X e. B /\ Y e. B ) -> ( ( X .o. Y ) e/ B -> M e/ Mgm ) ) with typecode |-
7	6	3impia	Could not format ( ( X e. B /\ Y e. B /\ ( X .o. Y ) e/ B ) -> M e/ Mgm ) : No typesetting found for |- ( ( X e. B /\ Y e. B /\ ( X .o. Y ) e/ B ) -> M e/ Mgm ) with typecode |-