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Metamath Proof Explorer

Theorem im1

Description: The imaginary part of one. (Contributed by Scott Fenton, 9-Jun-2006)

		Ref	Expression
	Assertion	im1	⊢ ( ℑ ‘ 1 ) = 0

Step	Hyp	Ref	Expression
1		1re	⊢ 1 ∈ ℝ
2		reim0	⊢ ( 1 ∈ ℝ → ( ℑ ‘ 1 ) = 0 )
3	1 2	ax-mp	⊢ ( ℑ ‘ 1 ) = 0