Theorem mgmcl

Description: Closure of the operation of a magma. (Contributed by FL, 14-Sep-2010) (Revised by AV, 13-Jan-2020)

	Ref	Expression
Hypotheses	mgmcl.b	$$⊢B={\mathrm{Base}}_M$$
	mgmcl.o	No typesetting found for |- .o. = ( +g ` M ) with typecode |-
Assertion	mgmcl	Could not format assertion : No typesetting found for |- ( ( M e. Mgm /\ X e. B /\ Y e. B ) -> ( X .o. Y ) e. B ) 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	ismgm	Could not format ( M e. Mgm -> ( M e. Mgm <-> A. x e. B A. y e. B ( x .o. y ) e. B ) ) : No typesetting found for |- ( M e. Mgm -> ( M e. Mgm <-> A. x e. B A. y e. B ( x .o. y ) e. B ) ) with typecode |-
4	3	ibi	Could not format ( M e. Mgm -> A. x e. B A. y e. B ( x .o. y ) e. B ) : No typesetting found for |- ( M e. Mgm -> A. x e. B A. y e. B ( x .o. y ) e. B ) with typecode |-
5		ovrspc2v	Could not format ( ( ( X e. B /\ Y e. B ) /\ A. x e. B A. y e. B ( x .o. y ) e. B ) -> ( X .o. Y ) e. B ) : No typesetting found for |- ( ( ( X e. B /\ Y e. B ) /\ A. x e. B A. y e. B ( x .o. y ) e. B ) -> ( X .o. Y ) e. B ) with typecode |-
6	5	expcom	Could not format ( A. x e. B A. y e. B ( x .o. y ) e. B -> ( ( X e. B /\ Y e. B ) -> ( X .o. Y ) e. B ) ) : No typesetting found for |- ( A. x e. B A. y e. B ( x .o. y ) e. B -> ( ( X e. B /\ Y e. B ) -> ( X .o. Y ) e. B ) ) with typecode |-
7	4 6	syl	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 |-
8	7	3impib	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 |-