Theorem mxidlnr

Description: A maximal ideal is proper. (Contributed by Jeff Madsen, 16-Jun-2011) (Revised by Thierry Arnoux, 19-Jan-2024)

	Ref	Expression
Hypothesis	mxidlval.1	$$⊢B={\mathrm{Base}}_R$$
Assertion	mxidlnr	Could not format assertion : No typesetting found for |- ( ( R e. Ring /\ M e. ( MaxIdeal ` R ) ) -> M =/= B ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		mxidlval.1	$$⊢B={\mathrm{Base}}_R$$
2	1	ismxidl	Could not format ( R e. Ring -> ( M e. ( MaxIdeal ` R ) <-> ( M e. ( LIdeal ` R ) /\ M =/= B /\ A. j e. ( LIdeal ` R ) ( M C_ j -> ( j = M \/ j = B ) ) ) ) ) : No typesetting found for |- ( R e. Ring -> ( M e. ( MaxIdeal ` R ) <-> ( M e. ( LIdeal ` R ) /\ M =/= B /\ A. j e. ( LIdeal ` R ) ( M C_ j -> ( j = M \/ j = B ) ) ) ) ) with typecode |-
3	2	biimpa	Could not format ( ( R e. Ring /\ M e. ( MaxIdeal ` R ) ) -> ( M e. ( LIdeal ` R ) /\ M =/= B /\ A. j e. ( LIdeal ` R ) ( M C_ j -> ( j = M \/ j = B ) ) ) ) : No typesetting found for |- ( ( R e. Ring /\ M e. ( MaxIdeal ` R ) ) -> ( M e. ( LIdeal ` R ) /\ M =/= B /\ A. j e. ( LIdeal ` R ) ( M C_ j -> ( j = M \/ j = B ) ) ) ) with typecode |-
4	3	simp2d	Could not format ( ( R e. Ring /\ M e. ( MaxIdeal ` R ) ) -> M =/= B ) : No typesetting found for |- ( ( R e. Ring /\ M e. ( MaxIdeal ` R ) ) -> M =/= B ) with typecode |-