Theorem bj-nfcri 32852

Description: Remove dependency on ax-ext 2602 (and df-cleq 2615) from nfcri 2758. (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 32851	. 2 ⊢ (𝑦 ∈ 𝐴 → ∀𝑥 𝑦 ∈ 𝐴)
3	2	nf5i 2024	1 ⊢ Ⅎ𝑥 𝑦 ∈ 𝐴

Syntax hints:  Ⅎwnf 1708   ∈ wcel 1990  Ⅎwnfc 2751

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clel 2618  df-nfc 2753

This theorem is referenced by:  bj-nfnfc  32853