Theorem basendx

Description: Index value of the base set extractor.

Use of this theorem is discouraged since the particular value 1 for the index is an implementation detail. It is generally sufficient to work with ( Basendx ) and use theorems such as baseid and basendxnn .

The main circumstance in which it is necessary to look at indices directly is when showing that a set of indices are disjoint, in proofs such as lmodstr . Although we have a few theorems such as basendxnplusgndx , we do not intend to add such theorems for every pair of indices (which would be quadradically many in the number of indices).

(New usage is discouraged.) (Contributed by Mario Carneiro, 2-Aug-2013)

	Ref	Expression
Assertion	basendx	$$⊢{\mathrm{Base}}_{\mathrm{ndx}}=1$$

Proof

Step	Hyp	Ref	Expression
1		df-base	$$⊢\mathrm{Base}=\mathrm{Slot}1$$
2		1nn	$$⊢1\in \mathbb{N}$$
3	1 2	ndxarg	$$⊢{\mathrm{Base}}_{\mathrm{ndx}}=1$$