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Metamath Proof Explorer

Theorem elfvexd

Description: If a function value has a member, then its argument is a set. Deduction form of elfvex . (An artifact of our function value definition.) (Contributed by David Moews, 1-May-2017)

		Ref	Expression
	Hypothesis	elfvexd.1	⊢ ( 𝜑 → 𝐴 ∈ ( 𝐵 ‘ 𝐶 ) )
	Assertion	elfvexd	⊢ ( 𝜑 → 𝐶 ∈ V )

Proof

Step	Hyp	Ref	Expression
1		elfvexd.1	⊢ ( 𝜑 → 𝐴 ∈ ( 𝐵 ‘ 𝐶 ) )
2		elfvex	⊢ ( 𝐴 ∈ ( 𝐵 ‘ 𝐶 ) → 𝐶 ∈ V )
3	1 2	syl	⊢ ( 𝜑 → 𝐶 ∈ V )