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Metamath Proof Explorer

Theorem baseval

Description: Value of the base set extractor. (Normally it is preferred to work with ( Basendx ) rather than the hard-coded 1 in order to make structure theorems portable. This is an example of how to obtain it when needed.) (New usage is discouraged.) (Contributed by NM, 4-Sep-2011)

		Ref	Expression
	Hypothesis	baseval.k	⊢ 𝐾 ∈ V
	Assertion	baseval	⊢ ( Base ‘ 𝐾 ) = ( 𝐾 ‘ 1 )

Proof

Step	Hyp	Ref	Expression
1		baseval.k	⊢ 𝐾 ∈ V
2		df-base	⊢ Base = Slot 1
3	1 2	strfvn	⊢ ( Base ‘ 𝐾 ) = ( 𝐾 ‘ 1 )