Theorem nfcriOLDOLDOLD 2895

Description: Obsolete version of nfcri 2888 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 2893	. 2 ⊢ (𝑦 ∈ 𝐴 → ∀𝑥 𝑦 ∈ 𝐴)
3	2	nf5i 2140	1 ⊢ Ⅎ𝑥 𝑦 ∈ 𝐴

Syntax hints:  Ⅎwnf 1783   ∈ wcel 2104  Ⅎwnfc 2881

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1911  ax-6 1969  ax-7 2009  ax-8 2106  ax-10 2135  ax-12 2169

This theorem depends on definitions:  df-bi 206  df-an 395  df-ex 1780  df-nf 1784  df-clel 2808  df-nfc 2883

This theorem is referenced by: (None)