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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 → ( 𝐹 ‘ ( 𝑁 + 1 ) ) = ( 𝐹 ‘ 1 ) )

Proof

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