This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem fv0p1e1

Description: Function value at N + 1 with N replaced by 0 . Technical theorem to be used to reduce the size of a significant number of proofs. (Contributed by AV, 13-Aug-2022)

		Ref	Expression
	Assertion	fv0p1e1	$⊢ N = 0 \to F (N + 1) = F (1)$

Proof

Step	Hyp	Ref	Expression
1		oveq1	$⊢ N = 0 \to N + 1 = 0 + 1$
2		0p1e1	$⊢ 0 + 1 = 1$
3	1 2	eqtrdi	$⊢ N = 0 \to N + 1 = 1$
4	3	fveq2d	$⊢ N = 0 \to F (N + 1) = F (1)$