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Metamath Proof Explorer

Theorem fvex

Description: The value of a class exists. Corollary 6.13 of TakeutiZaring p. 27. (Contributed by NM, 30-Dec-1996)

		Ref	Expression
	Assertion	fvex	⊢ ( 𝐹 ‘ 𝐴 ) ∈ V

Step	Hyp	Ref	Expression
1		df-fv	⊢ ( 𝐹 ‘ 𝐴 ) = ( ℩ 𝑥 𝐴 𝐹 𝑥 )
2		iotaex	⊢ ( ℩ 𝑥 𝐴 𝐹 𝑥 ) ∈ V
3	1 2	eqeltri	⊢ ( 𝐹 ‘ 𝐴 ) ∈ V