Theorem isclintop

Description: The predicate "is a closed (internal binary) operations for a set". (Contributed by FL, 2-Nov-2009) (Revised by AV, 20-Jan-2020)

	Ref	Expression
Assertion	isclintop	Could not format assertion : No typesetting found for |- ( M e. V -> ( .o. e. ( clIntOp ` M ) <-> .o. : ( M X. M ) --> M ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		clintopval	$$⊢M\in V\to \mathrm{clIntOp}\left(M\right)=M^{\left(M\times M\right)}$$
2	1	eleq2d	Could not format ( M e. V -> ( .o. e. ( clIntOp ` M ) <-> .o. e. ( M ^m ( M X. M ) ) ) ) : No typesetting found for |- ( M e. V -> ( .o. e. ( clIntOp ` M ) <-> .o. e. ( M ^m ( M X. M ) ) ) ) with typecode |-
3		sqxpexg	$$⊢M\in V\to M\times M\in \mathrm{V}$$
4		elmapg	Could not format ( ( M e. V /\ ( M X. M ) e. _V ) -> ( .o. e. ( M ^m ( M X. M ) ) <-> .o. : ( M X. M ) --> M ) ) : No typesetting found for |- ( ( M e. V /\ ( M X. M ) e. _V ) -> ( .o. e. ( M ^m ( M X. M ) ) <-> .o. : ( M X. M ) --> M ) ) with typecode |-
5	3 4	mpdan	Could not format ( M e. V -> ( .o. e. ( M ^m ( M X. M ) ) <-> .o. : ( M X. M ) --> M ) ) : No typesetting found for |- ( M e. V -> ( .o. e. ( M ^m ( M X. M ) ) <-> .o. : ( M X. M ) --> M ) ) with typecode |-
6	2 5	bitrd	Could not format ( M e. V -> ( .o. e. ( clIntOp ` M ) <-> .o. : ( M X. M ) --> M ) ) : No typesetting found for |- ( M e. V -> ( .o. e. ( clIntOp ` M ) <-> .o. : ( M X. M ) --> M ) ) with typecode |-