Theorem bj-nfcri 32046

Description: Remove dependency on ax-ext 2590 (and df-cleq 2603) from nfcri 2745. (Contributed by BJ, 6-Oct-2019.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-nfcri.1	⊢ Ⅎ𝑥𝐴

Assertion

Ref	Expression
bj-nfcri	⊢ Ⅎ𝑥 𝑦 ∈ 𝐴

Distinct variable group:   𝑥,𝑦

Allowed substitution hints:   𝐴(𝑥,𝑦)

Proof of Theorem bj-nfcri

Step	Hyp	Ref	Expression
1		bj-nfcri.1	. . 3 ⊢ Ⅎ𝑥𝐴
2	1	bj-nfcrii 32045	. 2 ⊢ (𝑦 ∈ 𝐴 → ∀𝑥 𝑦 ∈ 𝐴)
3	2	nf5i 2011	1 ⊢ Ⅎ𝑥 𝑦 ∈ 𝐴

Syntax hints:  Ⅎwnf 1699   ∈ wcel 1977  Ⅎwnfc 2738

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clel 2606  df-nfc 2740

This theorem is referenced by:  bj-nfnfc  32047