Theorem basendxnplusgndx

Description: The slot for the base set is not the slot for the group operation in an extensible structure. (Contributed by AV, 14-Nov-2021) (Proof shortened by AV, 17-Oct-2024)

	Ref	Expression
Assertion	basendxnplusgndx	$$⊢{\mathrm{Base}}_{\mathrm{ndx}}\ne {+}_{\mathrm{ndx}}$$

Proof

Step	Hyp	Ref	Expression
1		basendxnn	$$⊢{\mathrm{Base}}_{\mathrm{ndx}}\in \mathbb{N}$$
2	1	nnrei	$$⊢{\mathrm{Base}}_{\mathrm{ndx}}\in ℝ$$
3		basendxltplusgndx	$$⊢{\mathrm{Base}}_{\mathrm{ndx}}<{+}_{\mathrm{ndx}}$$
4	2 3	ltneii	$$⊢{\mathrm{Base}}_{\mathrm{ndx}}\ne {+}_{\mathrm{ndx}}$$