Theorem nfcrd

Description: Consequence of the not-free predicate. (Contributed by Mario Carneiro, 11-Aug-2016)

	Ref	Expression
Hypothesis	nfcrd.1	⊢ ( 𝜑 → Ⅎ 𝑥 𝐴 )
Assertion	nfcrd	⊢ ( 𝜑 → Ⅎ 𝑥 𝑦 ∈ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		nfcrd.1	⊢ ( 𝜑 → Ⅎ 𝑥 𝐴 )
2		nfcr	⊢ ( Ⅎ 𝑥 𝐴 → Ⅎ 𝑥 𝑦 ∈ 𝐴 )
3	1 2	syl	⊢ ( 𝜑 → Ⅎ 𝑥 𝑦 ∈ 𝐴 )