Theorem basendxnedgfndx

Description: The slots Base and .ef are different. (Contributed by AV, 21-Sep-2020)

	Ref	Expression
Assertion	basendxnedgfndx	⊢ ( Base ‘ ndx ) ≠ ( .ef ‘ ndx )

Proof

Step	Hyp	Ref	Expression
1		basendxnn	⊢ ( Base ‘ ndx ) ∈ ℕ
2	1	nnrei	⊢ ( Base ‘ ndx ) ∈ ℝ
3		baseltedgf	⊢ ( Base ‘ ndx ) < ( .ef ‘ ndx )
4	2 3	ltneii	⊢ ( Base ‘ ndx ) ≠ ( .ef ‘ ndx )