Theorem peano2cnm

Description: "Reverse" second Peano postulate analogue for complex numbers: A complex number minus 1 is a complex number. (Contributed by Alexander van der Vekens, 18-Mar-2018)

	Ref	Expression
Assertion	peano2cnm	⊢ ( 𝑁 ∈ ℂ → ( 𝑁 − 1 ) ∈ ℂ )

Proof

Step	Hyp	Ref	Expression
1		ax-1cn	⊢ 1 ∈ ℂ
2		subcl	⊢ ( ( 𝑁 ∈ ℂ ∧ 1 ∈ ℂ ) → ( 𝑁 − 1 ) ∈ ℂ )
3	1 2	mpan2	⊢ ( 𝑁 ∈ ℂ → ( 𝑁 − 1 ) ∈ ℂ )