Theorem nfcriOLDOLDOLD 2911

Description: Obsolete version of nfcri 2904 as of 23-May-2024. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
nfcriOLD.1	⊢ Ⅎ𝑥𝐴

Assertion

Ref	Expression
nfcriOLDOLDOLD	⊢ Ⅎ𝑥 𝑦 ∈ 𝐴

Distinct variable group:   𝑥,𝑦

Allowed substitution hints:   𝐴(𝑥,𝑦)

Proof of Theorem nfcriOLDOLDOLD

Step	Hyp	Ref	Expression
1		nfcriOLD.1	. . 3 ⊢ Ⅎ𝑥𝐴
2	1	nfcrii 2909	. 2 ⊢ (𝑦 ∈ 𝐴 → ∀𝑥 𝑦 ∈ 𝐴)
3	2	nf5i 2148	1 ⊢ Ⅎ𝑥 𝑦 ∈ 𝐴

Syntax hints:  Ⅎwnf 1786   ∈ wcel 2112  Ⅎwnfc 2897

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2114  ax-10 2143  ax-12 2176

This theorem depends on definitions:  df-bi 210  df-an 401  df-ex 1783  df-nf 1787  df-clel 2831  df-nfc 2899

This theorem is referenced by: (None)