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)

	Ref	Expression
Assertion	basendxnplusgndx	⊢ ( Base ‘ ndx ) ≠ ( +g ‘ ndx )

Proof

Step	Hyp	Ref	Expression
1		df-base	⊢ Base = Slot 1
2		1nn	⊢ 1 ∈ ℕ
3	1 2	ndxarg	⊢ ( Base ‘ ndx ) = 1
4		1ne2	⊢ 1 ≠ 2
5		plusgndx	⊢ ( +g ‘ ndx ) = 2
6	4 5	neeqtrri	⊢ 1 ≠ ( +g ‘ ndx )
7	3 6	eqnetri	⊢ ( Base ‘ ndx ) ≠ ( +g ‘ ndx )